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University  of  California  •  Berkeley 

The  Theodore  P.  Hill  Collection 

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Early  American  Mathematics  Books 


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THE 


First  Steps  in  Number. 


BY 


G.  A.  WENTWORTH,  A.M., 

PBOFESSOR  OF   MATHEMATICS   IN  PHILLIPS   EXETER  ACADEMY, 
AND 

E.  M.  REED, 

PRINCIPAL  OP  TRAINING   SCHOOL  AT   PLYMOUTH,   N.H. 


o;^o 


BOSTON: 
PUBLISHED   BY  GINN  &  COMPANY 
1891. 


Entered  according  to  Act  of  Congress,  in  the  year  1884,  by 

G.  A.  WENTWORTH  and  E.  M.  REED, 
in  the  Office  of  the  Librarian  of  Congress,  at  Washington. 


Typography  by  J.  S.  Cushinq  &  Co.,  Boston,  U.S.A. 


Presswork  bt  Ginn  &  Co.,  Boston,  U.S.A. 


PREFACE. 


THE  object  of  this  book  is  to  provide  teachers  with  a  record  of 
the  work  done  in  number  in  the  primary  schools  of  to-day. 

There  has  been  no  attempt  at  novelty  in  the  subject-matter,  in  the 
arrangement  of  work,  or  in  the  manner  of  presentation.  The  whole 
is  on  a  constructive  basis.  Numbers  are  chief;  processes  subordinate. 
What  has  been  found  to  be  more  easily  understood  precedes  the  more 
difficult,  without  respect  to  its  scientific  relation.  Fractions  present 
no  greater  difficulty  than  wholes,  so  they  accompany  the  teaching  of 
integral  numbers  from  the  beginning.  The  law  of  dependence  has 
been  carefully  observed,  although  at  first  glance  the  arrangement 
may  not  seem  to  warrant  this  assertion. 

The  object  of  every  teacher  is  so  to  present  numbers  that  the  mind 
of  the  child  may  grasp  firmly  the  facts  concerning  them,  and  hold 
these  facts  tenaciously  by  the  law  of  association.  Success  lies  in 
requiring  the  child  to  show  what  he  is  talking  about,  and  in  follow- 
ing the  "  step  by  step  "  rule.  The  book  illustrates  these  two  prin- 
ciples. It  abounds  in  examples  which  have  not  before  appeared  in 
print,  and  which  are  calculated  to  interest  the  child  from  their  close 
connection  with  his  varied  experiences.  It  gives  suggestions  for 
versatility  of  drill,  and  illustrates  in  detail  the  teaching  of  a  hun- 
dred topics. 

It  is  expected  that  the  work  to  the  number  ten  will  be  taken  in 
one  year,  the  work  to  twenty  in  another  year,  and  the  remainder  of 
the  course  outlined  in  the  book  will  be  covered  in  two  years  more. 

A  child's  book  accompanies  this  edition,  which  the  child  may  use 
with  great  advantage  after  he  becomes  acquainted  with  figures. 

It  is  hoped  that  this  book  will  find  a  welcome  among  all  persons 
interested  in  leading  children  by  easy  and  sure  paths  to  a  knowledge 
of  numbers. 

G.   A.   WENTWORTH. 
E.   M.   REED. 


TABLE  OF   CONTENTS. 


PAGE 

Chaptee  I.     Introduction 1 

Chapter  II.     The  Number  Three 5 

Chapter  III.     The  Number  Four 19 

Chapter  IV 34 

The  Number  Five,  34  ;  One-Half,  52. 

Chapter  V 55 

The  Number  Six,  55 ;  Pints  in  a  Quart,  85. 

Chapter  VI 87 

The  Number  Seven.  87 ;  Gills  in  a  Pint,  101. 

Chapter  VII 119 

The  Number  Eight,  119;  One-Fourth,  123. 
Chapter  VIII 153 

The  Number  Nine,  153;  One-Third,  196. 

Chapter  IX.     Figures 197 

Chapter  X. 212 

The  Number  Ten,  212 ;  The  Sign  of  Equality,  214 ;  The 
Sign  of  Addition,  217  ;  The  Sign  ol  Subtraction,  224. 

Chapter  XI.     The  Number  Eleven 228 

Chapter  XII 239 

The  Number  Twelve,  239;  The  Sign  of  Multiplication, 
254  ;  The  Foot,  255. 
Chapter  XIII.     The  Number  Thirteen 260 

Chapter  XIV 265 

The  Number  Fourteen,  265 ;  The  Sign  of  Division,  267 ; 
The  Yard,  280. 

Chapter  XV 282 

The  Number  Fifteen,  282;  The  Gallon,  289. 

Chapter  XVI.     The  Number  Sixteen 290 

Chapter  XVII 302 

The  Number  Seventeen,  302 ;  One-Sixth,  303. 
Chapter  XVIII.     The  Number  Eighteen        .        .        .        .305 

Chapter  XIX.     The  Number  Nineteen 311 

Chapter  XX.     Tens 314 

Chapter  XXI.     The  Number  Twenty      .         ...         .        .323 

Chapter  XXII.     The  Number  Twenty-One     ....     328 

Chapter  XXIII 333 

The  Number  Twenty-Four,  333;  One-Fifth,  339. 
Chapter  XXIV.     The  Number  Twenty-Five  ....     340 
Chapter  XXV.     The  Number  Twenty-Seven  ....     344 
Chapter  XXVL     The  Number  Twenty-Eight         .        .        .349 


Vi  TABLE   OF   CONTENTS. 

Chapter  XXVII 353 

The  Number  Thirty,  353 ;   United  States  Money,  360 ; 
Dry  Measures,  360. 
Chapter  XXVIII.    .        .        .        .        .        .        .        .        .    363 

First  Step  in  Addition,  363 ;  First  Step  in  Subtraction, 
364 ;  First  Step  in  Multiplication,  366. 

Chapter  XXIX 367 

The  Number  Thirty-Two,  367;  Ounces  in  a  Pound,  368; 
The  Number  Thirty-Five,  369;  The  Number  Thirty-Six, 
371;  Pecks  in  a  Bushel,  373;  The  Number  Forty,  374;  The 
Number  Forty-Two,  375;  The  Number  Forty-Five,  375; 
First  Step  in  Multiplying  Fractions,  376 ;  The  Number 
Forty-Eight,  376;  The  Number  Forty-Nine,  377. 

Chapter  XXX.         . 384 

Second  Step  in  Addition,  384;  Second  Step  in  Subtrac- 
tion, 385;  Second  Step  in  Multiplication,  386. 

Chapter  XXXI 387 

The  Number  Fifty-Four,  387;  The  Number  Fifty-Six, 
387 ;  The  Number  Sixty,  387 ;  A  Second  of  Time,  390;  Sec- 
onds in  a  Minute,  391 ;  Minutes  in  an  Hour,  392. 

Chapter  XXXII 394 

The  Number  Sixty-Three,  394;  The  Number  Sixty-Four, 
394 ;  Square  Numbers,  398 ;  Odd  and  Even  Numbers,  399. 

Chapter  XXXIII .    400 

The  Number  Seventy-Two,  400;  The  Number  Eighty- 
One,  400  ;  The  Rod,  405 ;  Yards  in  a  Rod,  406  ;  Rods  in  a 
Mile,  406 ;  Roman  Numerals,  407 ;  Combination  of  Roman 
Numerals,  408. 

Chapter  XXXIV 411 

The  Number  Eighty-Four,  411 ;  The  Number  Ninety- 
Six,  411. 

Chapter  XXXV .  •    41^ 

Third  Step  in  Multiplication,  418 ;  First  Step  in  Divis- 
ion, 420 ;  Second  Step  in  Division,  422. 

Chapter  XXXVI 429 

Reduction  of  Fractions,  429;  Addition  of  Fractions,  432; 
Multiplication  of  Fractions,^434 ;  Division  of  Fractions,  435. 

Chapter  XXXVII.  .       ' .442 

Factors  of  a  Number,  442 ;  Prime  and  Composite  Num- 
bers, 442 ;  Prime  Factors  of  a  Number,  443 ;  The  Greatest 
Common  Factor,  444 ;  A  Multiple  of  a  Number,  445 ;  The 
Least  Common  Multiple,  446. 

Chapter  XXXVIII 450 

Tenths,  450  ;  Tenths  and  Hundredths,  452. 

Chapter  XXXIX.     .        . 458 

Percentage,  458 ;  Commission  and  Brokerage,  465 ;  Inter- 
est, 467. 


FIRST  STEPS  11^  I^UMBER. 

CHAPTER  I. 

INTRODUCTION. 

Foe.  a  successful  teaching  of  Number  the  teacher  needs 
a  great  variety  of  objects.  Blocks,  splints,  sticks,  buttons, 
paper  patterns,  peas,  beans,  corn,  spools,  counters,  shells, 
pebbles,  horse-chestnuts,  acorns,  little  tin  plates,  cups  and 
saucers,  tin  money,  are  inexpensive  and  convenient  to  han- 
dle. For  measurements,  the  teacher  must  have  inch  meas- 
ures, foot  rules,  yard  measures,  a  set  of  tin  measures,  a  set 
of  wooden  or  paste-board  measures,  a  set  of  weights,  and  a 
pair  of  scales. 

The  teaching  of  Number  as  far  as  ten  does  not  include 
the  teaching  of  figures  or  other  signs  used  in  Arithmetic. 
No  blackboard  work  is  required  of  the  child  until  after  he 
has  learned  the  numbers  below  ten.  There  is  no  difficulty 
in  learning  the  figures  along  with  the  numbers ;  the  diffi- 
culty comes  in  learning  the  numbers  along  with  the  figures. 
So  it  seems  best  to  ignore  the  sign  in  favor  of  the  thing. 

It  is  more  convenient  in  these  exercises  to  have  the  chil- 
dren stand  about  a  table  on  which  are  the  objects  to  be 
handled,  and  many  of  the  directions  to  the  class  are  given 
with  this  arrangement  in  view.  Let  the  children  illustrate 
each  story  with  objects,  until  it  is  evident  that  the  relation 
between  the  numbers  is  as  clearly  seen  without  the  objects 
as  with  them.  Whenever  a  mental  picture  is  formed,  then 
the  material  is  a  hindrance  to  the  teaching.     Objects  are  a 


2  FIRST  STEPS   IN   NUMBER. 

means  to  an  end,  not  the  end.  When  an  idea  has  been 
abstracted  from  the  concrete,  objects  no  longer  have  an 
office  to  perform,  and  should  be  put  aside. 

Ascertain  the  child's  knowledge  of  Number  before  at- 
tempting any  teaching  of  Number.  Do  this  by  skilful 
examination  after  the  child  feels  at  home  in  the  school- 
room. 

"Show  me  so  many  blocks  (two  blocks);  so  many  beans; 
so  many  pebbles  ;  so  many  spools  ;  so  many  pencils." 

"How  many  blocks  have  I  in  my  hand?  Come,  whisper 
to  me,  if  you  know." 

After  each  has  whispered  the  number,  ask  the  class : 

"How  many  spools  did  you  show  me?  how  many  beans? 
how  many  blocks  ?  " 

Let  the  class  answer  in  concert,  "Two,"  each  time. 

"  Show  me  two  buttons  ;  two  boys  ;  two  girls  ;  two  chairs." 

"Put  two  blocks  on  the  table  in  front  of  you;  put  two 
buttons  on  the  table ;  take  one  button  from  the  table  and 
•put  it  under  the  table ;  put  one  block  under  the  table." 

If  two  be  known,  try  three,  and  so  on  until  a  number  is 
reached  which  is  not  known. 

Second  step  in  the  examination  : 

Require  the  child  to  show  some  number  with  which  he  is 
familiar.     For  example,  two. 

"  Take  one  of  your  two  blocks  away.  How  many  blocks 
have  you  left?" 

"If  I  have  two  horses  and  sell  one  horse,  how  many 
horses  shall  I  then  have?" 

"If  I  have  two  pencils  and  lose  one  pencil,  how  many 
pencils  have  I  left?" 

"You  may  put  one  block  on  the  table  in  front  of  you. 
You  may  put  another  block  with  it.  How  many  blocks 
have  you  now  shown  me  ?  " 

"  One  block  and  one  block  are  how  many  blocks  ?  " 


INTRODUCTION.  3 

"One  horse  and  one  horse  are  how  many  horses?  " 

"  If  I  have  one  pencil  and  buy  another,  how  many  pencils 
shall  I  have?" 

*'  If  John  has  one  cent  and  I  give  him  another  cent,  how 
many  cents  will  he  have  ?  " 

"If  Susie  has  one  apron  and  mamma  makes  her  another, 
how  many  aprons  will  Susie  have?" 

"Show  me  two  buttons.  Take  the  two  buttons  away. 
How  many  buttons  remain  ?  " 

"  If  there  are  two  cows  in  the  barn  and  two  cows  are 
turned  out  in  the  yard,  how  many  cows  remain  in  the 
barn?" 

"  Show  me  two  boxes.  Put  one  block  in  each  box.  How 
many  blocks  does  it  take?" 

"If  these  two  little  girls  have  each  a  doll,  how  many 
dolls  have  they  together?" 

"  If  these  two  little  boys  have  each  a  sled,  how  many 
sleds  have  they  together?" 

"  II  there  are  two  nests,  and  an  egg  in  each  nest,  how 
many  eggs  are  there?" 

"  If  there  are  two  stores,  and  a  wagon  at  each  store,  how 
many  wagons  are  there  ? 

"  Show  me  two  blocks.  Put  one  of  these  two  blocks  in 
this  box.  Put  another  of  your  blocks  in  this  box.  How 
many  boxes  does  it  take  ?  " 

"  If  you  have  two  hens,  and  each  sits  in  a  nest  by  her- 
self, how  many  nests  will  it  take?" 

"  If  you  have  two  spoons,  and  put  each  into  a  cup  by 
itself,  how  many  cups  will  it  take?" 

"  If  you  have  two  cents,  and  give  one  each  Sunday,  how 
many  Sundays  can  you  give  before  the  two  cents  will  be 
given  away?" 

"If  you  have  two  pencils,  and  put  each  on  a  slate  by 
itself,  on  how  many  slates  will  you  put  them?" 


4  FIRST  STEPS  IN   NUMBER. 

This  outline  for  review  is  merely  suggested  as  being 
searching  in  its  nature.  The  aim  should  be  solely  to  bring 
to  light  all  the  child's  knowledge  of  Number,  that  the 
teacher  may  waste  no  time  upon  teaching  him  what  he 
already  knows.  Do  not  hurry  the  examination.  See  that 
each  child  does  for  himself  what  you  require,  and  does  not 
imitate  you  or  his  neighbor  in  his  work.  Let  each  one 
answer  for  himself.  Distinguish  between  the  child's  failure 
to  understand  your  language  and  his  inability  to  do  what 
you  require  of  him. 

When  the  examination  is  complete,  begin  the  teaching, 
and  take  the  child  where  he  is.  As  far  as  the  experience 
of  most  primary  teachers  goes,  few  children  know  beyond 
two  when  they  enter  school  for  the  first  time.  In  most 
instances  three  will  be  the  starting-point  in  teaching. 

The  ability  to  count  up  to  a  number  does  not  constitute 
a  knowledge  of  the  number ;  so  this  must  not  be  taken  as 
the  test  of  the  child's  knowledge.  Do  not  permit  counting 
by  ones  throughout  the  work  in  Arithmetic. 

In  the  teaching  of  every  number  the  order  to  be  observed 
is  as  follows : 

I.    The  perception  of  the  number. 
II.    Analysis  of  the  number. 

III.  Drill  upon  facts  discovered  by  analysis. 

IV.  Comparison  with  smaller  numbers. 


OHAPTEE  II. 

THE    NUMBER    THREE. 


§  1.   Three  as  a  Whole. 

Show  me  two  blocks.     Put  one  more  block  with  them. 

Show  me  just  as  many  spools ;  just  as  many  pebbles ;  as 
many  buttons ;  as  many  pencils ;  as  many  marks  on  the 
board  ;  as  many  fingers. 

You  have  shown  me  three  fingers. 

Show  me  three  marks  you  have  made  on  the  board  ; 
three  spools  ;  three  pencils ;  three  pebbles  ;  three  shells  ; 
three  little  girls  ;  three  boys ;  three  blocks. 

How  many  blocks  have  you  shown  me?  How  many 
spools  ?  '  How  many  splints  ?     How  many  buttons  ? 

I  have  a  block,  a  spool,  and  a  nut.     How  many  things? 

I  have  a  box,  a  pen,  and  a  stick.     How  many  things? 

Show  me  a  button,  a  nut,  and  a  shell.  How  many  things 
have  you  shown  me  ? 

Show  me  three  other  things.  Go  to  your  d^sk  and  bring 
me  three  things. 

Who  thinks  he  has  seen  three  men  on  the  street  ?  three 
boys  playing  ball  ?  three  houses  in  a  row  ?  three  horses 
drawing  a  load  ?  three  street  cars  in  a  row  ?  three  people 
in  a  carriage  ?  three  things  in  the  shop  window  ? 

Name  three  things  you  saw  on  your  way  to  school ;  three 
things  you  had  for  breakfast ;  three  things  you  can  do  ; 
three  things  you  can  wear ;  three  things  you  own  ;  three 
persons  you  know. 


6  FIRST  STEPS   IN   NUMBER 

§2.   Discoveries  in  Three. 

You  may  take  one  block  away  from  your  three  blocks. 
How  many  blocks  have  you  left  ?  What  else  can  you  take 
away  from  three  blocks  ?  How  many  blocks  will  remain  ? 
What  other  number  can  you  take  away?  What  will 
remain  ? 

Who  sees  something  else  that  can  be  done  ?  I  see  Mary 
has  put  hers  in  two  groups.  How  many  in  this  group? 
(Two.)  How  many  in  this  ?  (One.)  What  did  Mary  find 
in  three  ?     (Two  blocks  and  one  block.) 

Who  can  find  anything  else  ? 


§  3.   Facts  in  Three. 
Two  and  One. 

You  may  each  take  two  blocks.  Take  one  more  block. 
How  many  blocks  are  two  blocks  and  one  block  ? 

Show  me  two  shells.  Show  me  one  more  shell.  How 
many  shells  have  you  shown  me  ? 

Show  me  two  beads  and  one  bead.  How  many  beads 
are  two  beads  and  one  more  bead? 

Show  me  two  pegs  and  one  more  peg.  How  many  pegs 
have  you  shown  me  ? 

In  these  envelopes  are  pretty  things.  I  will  give  each 
of  you  an  envelope  if  you  will  try  to  take  out  just  two 
things,  and  then  one  more.  Mary,  tell  me  about  your 
dustpans.  Henry,  about  your  rakes.  Annie,  about  your 
combs.  John,  about  your  knives.  Nellie,  about  your 
birds. 

We  will  call  these  beautiful  red  strips  of  paper  sticks  of 
candy.  Who  will  tell  me  about  two  sticks  of  candy  and 
one  more  stick  of  candy  ? 


THE   NUMBER   THREE.  7 

If  you  take  two  splints  (let  the  child  take  the  two  splints) 
and  one  more  splint  (let  this  be  taken  also),  how  many- 
splints  have  you  ?     Tell  me  that  story. 

Mary,  if  you  take  two  buttons  and  then  take  one  more, 
how  many  buttons  have  you  ?     Tell  me  a  story  about  that. 

Tell  me  a  story  about  two  shells  and  one  shell ;  about 
two  pencils  and  one  pencil. 

I  am  going  to  call  my  blocks  horses.  If  I  have  two 
horses  and  buy  one  more  horse,  I  shall  have  three  horses. 

Kemaek.  In  telling  a  story,  always  handle  the  blocks  so  as  to 
illustrate  what  is  being  said,  and  require  the  pupil  to  do  the  same. 

What  will  you  call  your  blocks?  You  may  tell  me  the 
story  that  two  kitties  and  one  kitty  are  three  kitties. 

One  and  Two. 

Show  me  one  block.  Show  me  two  more  blocks.  How 
many  blocks  have  you  shown  me  ? 

Show  me  one  wheel.  Show  me  two  more  wheels.  How 
many  wheels  are  one  wheel  and  two  wheels  ? 

If  I  have  one  beautiful  butterfly,  and  find  two  more 
butterflies,  how,  many  butterflies  shall  I  have  ? 

How  many  owls  are  one  owl  and  two  owls  ? 

If  I  have  one  shell  and  take  two  more  shells,  how  many 
shells  shall  I  have  ? 

I  will  hold  up  one  finger ;  now  I  will  hold  up  two  more 
fingers.     How  many  fingers  do  I  hold  up  ? 

I  will  take  one  piece  of  paper  and  then  take  two  more 
pieces  of  paper.     I  shall  then  have  three  pieces  of  paper. 

You  may  tell  me  a  story  like  this  with'  your  blocks ; 
with  these  buttons  ;  with  your  fingers  ;  with  these  nuts. 

I  will  call  my  blocks  birds.  Here  is  one  bird  on  a  tree, 
and  two  more  birds  fly  up  on  the  same  tree.  Tell  me  how 
many  birds  are  on  the  tree. 


8  FIRST  STEPS   IN   NUMBER. 

This  is  a  dog  running,  and  these  are  two  little  girls  run- 
ning after  him.     How  many  are  running? 

You  may  tell  me  a  story  about  one  and  two.  What  will 
you  call  your  blocks  ?     Another  story ;  another. 

Tell  me  about  one  urmful  of  wood  and  two  armfuls  of 
wood ;  one  knife  and  two  knives ;  one  chair  and  two  chairs  ; 
one  tin  horn  and  two  tin  horns ;  one  whistle  and  two  whis- 
tles ;  one  paper-weight  and  two  paper-weights. 

If  one  child  tells  me  a  story  about  birds,  and  two  others 
tell  me  stories  about  birds,  how  many  tell  me  stories  about 
birds  ? 

If  I  write  one  word  on  the  blackboard,  and  then  write 
two  more  words  on  the  blackboard,  how  many  words  do  I 
write  in  all  ? 

Daisy  saw  one  dog  on  one  side  of  the  street  this  morning, 
and  two  more  dogs  the  other  side  of  the  street.  How  many 
dogs  did  she  see  on  the  street  ? 

On  one  twig  is  a  white  blossom  and  two  pink  blossoms. 
How  many  blossoms  on  the  twig  ? 

I  have  a  woollen  cap  and  two  hats.  How  many  things 
have  I  to  wear  on  my  head  ? 

Three  minus  One. 

Show  me  three  blocks.  Do  as  I  do.  (Teacher  puts  one 
of  her  three  blocks  away.)    How  many  have  you  left  ? 

How  many  did  you  take  away  ? 

Show  me  your  three  blocks  again. 

Take  one  block  away.     How  many  have  you  now  ? 

Show  me  your  three  blocks  again. 

I  have  three  blocks  on  the  table.  I  will  put  one  block 
under  the  table.     How  many  blocks  have  I  on  the  table  ? 

You  may  tell  me  a  story  about  this.  You  may  tell  me  a 
story  with  the  splints ;  with  the  spools ;  with  the  tin  plates. 


THE   NUMBER   THREE.  9 

If  I  have  three  cows,  and  sell  one,  how  many  cows  shall 
I  have  left? 

If  I  have  three  beds  to  make,  and  make  one,  how^  many 
more  beds  shall  I  have  to  make  ? 

If  you  have  three  cups  to  wipe,  and  wipe  one,  how  many 
more  cups  will  you  have  to  wipe  ? 

If  you  have  three  lines  of  ^'s  to  write,  and  write  one  line, 
how  many  more  lines  must  you  write? 

Three  minus  Tvvo. 

Take  three  blocks.  Give  me  two  of  them.  How  many 
have  you  left  ? 

How  many  did  you  give  me  ?  I  will  give  you  back  the 
two  blocks. 

Put  two  of  your  blocks  behind  you  ?  How  many  remain 
before  you  ? 

How  many  did  you  take  away  ? 

Show  me  your  three  blocks  again. 

If  I  have  three  blocks,  and  give  you  two  of  my  blocks,  I 
shall  have  one  block  left. 

You  may  tell  me  the  same  kind  of  a  story  with  these 
buttons ;  with  these  beads ;  with  these  cents ;  with  these 
keys. 

Go  to  the  board  and  make  three  marks.  Erase  two 
marks.     How  many  remain  ? 

Hold  up  three  fingers.  Shut  two  of  the  fingers.  How 
many  fingers  remain  up  ? 

If  mamma  has  three  pies  to  make,  and  makes  two,  how 
many  more  must  she  make  ? 

If  two  of  the  three  pies  get  burned,  how  many  will  not 
be  burned  ? 

If  three  boys  are  in  a  line,  and  two  boys  step  out  of  the 
line,  how  many  remain  in  the  line? 


10  FIRST   STEPS   IN   NUMBER. 

If  you  have  three  cents,  and  buy  peanuts  with  two  cents, 
how  many  cents  will  you  then  have  ? 

If  three  sleds  are  going  down  the  hill,  and  two  tip  over, 
how  many  go  down  the  hill  ? 

If  there  are  three  chairs  up  to  the  table,  and  you  set  back 
two  chairs,  how  many  chairs  will  remain  up  to  the  table  ? 

Exercise  for  Review. 

If  Jamie  catches  two  mice  one  day  and  one  mouse  another 
day,  how  many  mice  will  he  catch  in  all  ? 

I  have  in  my  hand  a  button,  a  stick,  and  a  tin  cent. 
How  many  things  have  I  in  my  hand  ? 

I  have  on  my  bureau  a  cologne-bottle,  a  pin-cushion,  and 
a  watch-stand.     How  many  things  have  I  on  my  bureau  ? 

If  I  should  put  the  watch-stand  on  the  table,  how  many 
things  would  be  left  on  the  bureau  ? 

If  I  should  put  the  cologne-bottle  on  the  mantel,  how 
many  things  would  remain  on  the  bureau  ? 

If  I  carried  back  the  watch-case  and  cologne-bottle,  how 
many  things  would  there  be  on  the  bureau  ? 

Our  baby  is  two  years  old.  How  old  will  she  be  in  a 
year? 

Here  are  three  boxes ;  if  you  put  a  block  in  each  box, 
how  many  blocks  will  it  take  ? 

One  boy  and  one  boy  are  how  many  boys  ? 

One  chicken  and  one  chicken  are  how  many  chickens? 

One  boy  and  one  girl  are  how  many  persons  ? 

Two  kittens  and  a  dog  are  how  many  animals  ? 

A  mouse  comes  into  the  room  to  find  something  to  eat. 
A  cat  comes  into  the  room  to  find  what  she  can  eat.  How 
many  animals  are  in  the  room  ?  The  cat  and  mouse  both 
run  into  Mary's  room,  where  she  is  sitting.  How  many 
are  running  then,  do  yo\i  think  ? 


THE   NUMBER   THREE.  H 


Three  divided  by  One. 

Show  me  three  blocks. 

Show  ine  one  of  your  three  blocks. 

Show  me  another  of  your  three  blocks. 

How  many  have  you  shown  me  now  ? 

Show  me  another  of  your  three  blocks. 

How  many  one-blocks  have  you  found  in  three  blocks? 

Take  three  buttons. 

How  many  one-buttons  can  you  find  in  three  buttons? 

Take  three  pencils. 

How  many  one-pencils  can  you  find  in  three  pencils  ? 

Mary  may  take  three  sticks,  and  give  one  to  as  many 
little  girls  as  she  has  sticks  for. 

To  how  many  little  girls  can  she  give  them  ? 

Take  three  buttons,  and  divide  them  in  the  same  way. 
To  how  many  can  you  give  them?  Three  cents ;  three  ap- 
ples; three  beads. 

Take  three  books.  Put  each  book  on  a  desk  by  itself. 
How  many  desks  does  it  take? 

Take  three  pencils,  and  put  each  pencil  on  a  slate  by  itself. 
How  many  slates  does  it  take  ? 

Here  are  three  spools.  Put  each  one  on  a  book  by  itself. 
How  many  books  does  it  take  ? 

Take  three  splints,  and  put  each  one  in  a  box  by  itself. 
How  many  boxes  does  it  take  ? 

Take  three  buttons,  and  put  each  in  a  box  by  itself.  How 
many  boxes  does  it  take  ? 

Take  three  erasers.  Put  each  one  at  a  board  by  itself. 
How  many  boards  does  it  take? 

Here  are  three  little  girls.  Each  one  may  go  ajid  sit  at 
a  desk  by  herself.  How  many  desks  does  it  take  ?  How 
many  chairs? 


12  FIRST   STEPS   IN   NUMBER. 

If  there  are  three  cups,  and  you  put  each  in  a  saucer  by 
itself,  how  many  saucers  will  it  take? 

If  you  have  three  spoons,  and  put  each  one  in  a  cup  by 
itself,  how  many  cups  will  have  a  spoon  ? 

You  may  tell  me  a  story  like  this  about  the  spoons ; 
another;  another;  another;  another. 

Three  Ones. 

Here  are  three  baskets.  You  may  put  a  kitty  in  each 
basket.     How  many  kitties  are  in  all  the  baskets  ? 

Here  are  three  nests.  Put  an  egg  in  each  nest,  and 
tell  me  how  many  eggs  it  takes. 

Here  are  three  little  girls.  Give  each  a  pencil,  and  tell 
me  how  many  pencils  it  takes. 

Here  are  three  plates.  Put  an  apple  on  each  plate,  and 
tell  me  how  many  apples  it  takes. 

Here  are  three  posts,  with  a  horse  at  each  post.  How 
many  horses  do  you  see  ? 

Show  me  three  pens,  wdth  a  pig  in  each  pen.  How 
many  pigs  do  you  show  me  ? 

Show  me  three  lamp-posts,  with  one  lamp  on  each  post. 
How  many  lamps  do  you  show  me  ? 

Show  me  three  dustpans,  with  a  brush  in  each  pan,  and 
tell  me  how  many  brushes  you  show  me. 

If  each  brush  has  a  handle,  how  many  handles  do  three 
brushes  have  ? 

How  many  noses  do  three  little  boys  have? 

How  many  heads  do  three  pins  have  ? 

How  many  handles  do  three  pitchers  have  ? 

You  may  show  me  three  boxes,  with  a  button  in  each 
box.     How  many  buttons  do  you  show  me  ? 

You  may  show  me  three  pieces  of  paper,  with  a  pin  in 
each  paper.     How  many  pins  do  you  show  me  ? 


THE   NUMBER   THREE.  13 

Show  me  three  hats.  How  many  bands  on  each  hat? 
How  many  bands  on  the  three  hats  together? 

Show  me  three  boys,  each  with  a  hat  on  his  head.  How 
many  hats  does  it  take  for  the  three  boys  ? 

If  I  have  three  boxes,  and  a  block  in  each  box,  how  many 
blocks  shall  I  have  ? 

If  I  have  three  books,  and  each  book  has  a  picture  in  it, 
how  many  pictures  shall  I  have  to  look  at? 

If  these  three  boys  each  give  me  a  cent,  how  many  cents 
shall  I  have? 

If  there  are  three  nests,  and  an  egg  in  each  nest,  how 
many  eggs  are  there  ? 

If  there  are  three  stalls,  and  a  horse  in  each  stall,  how 
many  horses  are  there  ? 

If  there  are  three  slates,  and  a  pencil  on  each  slate,  how 
many  pencils  are  there  ? 

If  there  is  a  bed  in  each  room,  how  many  beds  will  there 
be  in  three  rooms  ? 

If  there  is  a  candle  in  each  candle-stick,  how  many  can- 
dles in  three  candle-sticks  ? 

Exercise  for  Review. 

Charlie  has  two  marbles  and  a  kite.  How  many  things 
has  he  ? 

Nellie  has  a  kitten  and  two  dolls.  How  many  things  has 
she? 

Jamie  bought  three  pencils  this  morning,  but  has  broken 
one  already.     How  many  whole  pencils  has  he  ? 

There  were  three  blossoms  on  this  twig,  but  two  have 
fallen  off.     How  many  are  left? 

There  are  three  desks,  with  a  pencil  on  each  desk.  How 
many  pencils  are  there  ? 

Here  are  three  boys,  each  with  an  apple.  How  many 
apples  are  there  ? 


14  FIRST  STEPS   IN   NUMBER. 

Tom  had  three  oranges,  but  gave  one  to  each  of  his  two 
little  brothers.     How  many  oranges  had  he  then  ? 
Two  boys  and  one  boy  are  how  many  boys  ? 
One  girl  and  two  girls  are  how  many  girls  ? 
Three  cents  minus  two  cents  are  how  many  cents  ? 
Three  blocks  minus  one  block  are  how  many  blocks  ? 

Three  minus  Three. 

Show  me  three  marks  on  the  board  ?  Erase  the  three 
marks.       How   many  remain  ? 

Show  me  three  pieces  of  crayon.  Give  me  the  three 
pieces  of  crayon.     How  many  pieces  have  you  ? 

Here  are  three  buttons.  Put  them  in  your  pocket.  How 
many  buttons  do  you  see  now  ? 

Here  are  three  kittens  asleep.  Wake  the  three  kittens. 
How  many  are  asleep  now  ? 

If  you  have  three  balls,  and  lose  three,  how  many  balls 
will  you  have  left  ? 

Tell  me  that  story  with  these  spools ;  these  pictures ; 
these  pencils  ;  these  counters  ;  these  beans  ;  these  splints  ; 
these  shells. 

If  there  are  three  doves  on  the  roof,  and  the  three  doves 
fly  down  on  the  ground,  how  many  doves  are  on  the  roof 
then  ? 

If  there  are  three  sticks  of  wood  in  the  wood-box,  and 
you  put  three  sticks  of  wood  in  the  stove,  how  many 
sticks  remain  in  the  box  ? 

If  there  are  three  plums  on  your  plate,  and  you  eat  the 
three  plums,  how  many  plums  remain  on  your  plate  ? 

Tell  me  a  story  about  three  cents  minus  three  cents ;  three 
knives  minus  three  knives  ;  three  chairs  minus  three  chairs ; 
three  quarts  of  berries  minus  three  quarts  of  berries  ;  three 
kittens  minus  three  kittens ;  three  leaves  minus  three  leaves. 


THE   NUMBER  THREE.  15 

§4.   Comparison  of  Three  with  Numbers  Known. 

Take  two  blocks.  How  many  more  must  you  take  to 
have  three  blocks  ? 

Take  two  buttons.  How  many  more  must  you  take  to 
have  three  buttons  ? 

If  you  have  two  sticks  of  candy,  how  many  sticks 
of  candy  must  I  give  you  that  you  may  have  three 
sticks  ? 

If  you  jump  twice,  how  many  more  times  must  you  jump 
to  jump  three  times? 

Take  one  block.  How  many  more  must  you  take  to 
have  three  blocks  ? 

If  I  have  three  cents,  and  you  have  one,  how  many 
more  have  I  than  you  ? 

Annie  has  one  doll ;  Mary  has  three  dolls.  How  many 
more  dolls  has  Mary  than  Annie  ? 

Jamie  has  one  pencil ;  I  have  three  pencils.  How  many 
more  pencils  have  I  than  Jamie  ? 

Harry  has  three  words  to  copy  ;  he  has  copied  one.  How 
many  more  words  has  he  to  copy  ? 

I  have  a  three-pint  pail.  If  there  is  one  pint  of  berries 
in  it,  how  many  more  pints  of  berries  can  I  put  in  it  before 
it  is  full  ? 

Show  me  one  block.  Show  me,  just  below  the  one  block, 
two  blocks.     Show  me  three  blocks  just  below  these. 

Which  row  has  the  most  blocks  ? 

Which  row  has  the  least  blocks  ? 

How  many  more  in  the  middle  row  than  in  the  first  row  ? 

How  many  less  than  in  the  last  row  ? 

How  many  more  in  the  three-row  than  in  the  one-row  ? 
than  in  the  two-row? 

How  many  less  in  the  one-row  than  in  the  two-row? 
than  in  the  three-row  ? 


16  FIRST  STEPS  IN   NUMBER. 


Exercise  for  Revie^v. 


Lay  down  one  counter  and  one  block.  How  many  things 
have  you  laid  down  ? 

Lift  up  your  foot  three  times. 

How  many  cups  at  tea-time  must  be  put  out  for  you  and 
me  ?     Show  me  with  these  cups. 

Take  three  steps  forward. 

Take  two  steps  backward. 

How  many  joints  has  your  thumb?  your  forefinger? 

I  have  put  one  cent  on  the  table.  Put  enough  with  it  to 
make  three  cents. 

Nod  your  head  twice  and  then  once ;  how  many  times 
have  you  nodded  it? 

Shut  your  hand  ;  open  one  finger ;  another  finger.  How 
many  fingers  have  you  now  open  ?  Open  enough  more  to 
make  three. 

Show  me  three  legs  of  a  chair. 

Hold  out  three  fingers. 

Show  me  two  shells  ;  now  show  me  another.  How  many 
shells  have  you  shown  me  ? 

Say  ''one"  for  each  shell  you  have  shown  me. 

Tap  the  table  once;  again;  again.  How  many  times 
have  you  tapped  it  ? 

How  many  hands  have  you  ? 

How  many  eyes  have  you?  ears?  elbows? 

Show  me  your  wrists.     How  many  have  you  ? 

Show  me  your  cheeks.    How  many  have  you  ? 

Show  me  your  feet.     How  many  have  you  ? 

Tell  me  two  things  you  can  do. 

Tell  me  two  things  you  did  this  morning ;  two  things 
you  saw  coming  to  school. 

Tell  me  two  kinds  of  food  you  ate  for  breakfast ;  two 
things  you  always  jDut  on  the  table  when  you  set  it. 


THE    NUMBER   THREE.  17 

Show  me  two  apples ;  put  one  in  the  drawer.  How 
many  apples  are  left? 

Tell  me  a  story  about  two ;  another  ;  another  ;  another ; 
another ;  another. 

You  may  copy  the  word  two  on  your  slate. 

How  many  mouths  have  you  ?  how  many  chins  ? 

How  many  heads  have  you  ? 

How  many  heads  have  two  little  boys? 

How  many  tongues  have  two  little  boys  ? 

If  two  little  girls  have  each  an  apple,  how  many  apples 
have  both  together  ? 

If  I  had  three  pieces  of  pie,  and  should  put  each  piece 
on  a  plate  by  itself,  how  many  plates  would  it  take  ? 

If  there  are  three  of  you  at  the  table,  and  I  give  each  of 
you  a  saucer  of  strawberries,  how  many  saucers  of  straw- 
berries will  it  take  ? 

If  I  should  give  each  of  three  little  girls  a  flower,  how 
many  flowers  would  it  take? 

If  I  have  a  knife,  a  pencil,  and  a  key  in  my  pocket,  how 
many  things  have  I  in  my  pocket  ? 

How  many  children  are  two  girls  and  one  boy  ? 

If  one  of  these  children  should  run  away,  how  many 
would  remain  ? 

If  one  more  should  go  home,  how  many  would  be  left  ? 

If  I  have  three  nuts,  and  eat  three  nuts,  how  many  nuts 
shall  I  have  ? 

Tell  me  a  story  about  this  ;  another  ;  another  ;  another ; 
another ;  another. 

If  three  birds  have  each  a  worm,  how  many  worms  have 
the  birds  together  ? 

I  have  here  two  buttons.  If  I  put  one  on  a  sleeve  by 
itself,  how  many  sleeves  can  I  put  them  on  ? 

Put  a  pencil  on  each  of  these  slates  (three).  How  many 
pencils  does  it  take  ? 


18  FIRST   STEPS   IN   NUMBER. 

If  you  make  a  mark  on  your  slate  for  each  door  in  thic 
room,  how  many  marks  will  you  make  ? 

If  you  make  a  mark  for  each  door  in  your  room  at  home, 
how  many  marks  must  you  make  ? 

If  you  make  a  mark  for  each  chair  in  your  room,  how 
many  marks  will  you  make  ? 

Mary,  you  may  make  a  mark  on  your  slate  for  yourself 
and  your  little  brother.  How  many  are  yourself  and  little 
brother?     How  many  marks,  then,  will  you  make? 

At  home,  I  have  two  boxes  on  the  top  of  my  bureau,  and 
a  comb  in  each  box  ;  how  many  combs  are  there  ? 

Clapp  your  hands  twice,  then  once.  How  many  times 
have  you  clapped  your  hands  ? 

Three  kittens  are  how  many  more  than  one  kitten  ? 

Three  kittens  are  how  many  more  than  two  kittens  ? 

One  duck  and  two  ducks  are  how  many  ducks? 

Two  dogs  are  how  many  more  than  one  dog? 

Two  chickens  and  one  chicken  are  how  many  chickens? 

A  bird  has  how  many  wings?  how  many  eyes?  how 
/nany  feet?  how  many  tails? 

If  you  have  a  knife,  a  fork,  and  a  spoon,  how  many 
things  have  you  ? 

How  many  more  things  are  a  knife  and  a  fork  than  two 
spoons. 

Write:  ^  %^  ••• 

one.  two.  three. 


CHAPTEE  III. 

THE    NUMBER    FOUR. 


§  5.     Four  as  a  Whole. 

Show  me  three  fingers ;  open  another  finger. 

Look  at  the  number  of  fingers  you  have  shown  me. 

Show  me  as  many  children ;  as  many  chairs ;  as  many 
books  ;   as  many  buttons  ;  as  many  pieces  of  paper. 

Here  are  four  pieces  of  paper. 

How  many  pieces  of  paper  did  you  show  me  ? 

How  many  fingers  do  I  show  you  ?  how  many  blocks  ? 

Show  me  four  blocks ;  four  marks  on  the  board ;  four 
erasers  ;  four  balls ;  four  keys  ;  four  pencils ;  four  is  ;  four 
boxes. 

How  many  thumbs  are  your  thumbs  and  my  thumbs? 

How  many  forefingers  are  your  forefingers  and  my  fore- 
fingers ? 

How  many  ears  have  these  two  little  boys? 

How  many  joints  have  both  your  thumbs? 

Give  the  names  of  four  boys  you  know. 

Name  something  that  has  four  legs ;  something  else ; 
something  else  ;  something  else  ;  something  else. 

Where  have  you  seen  four  houses  ?  four  thimbles  ?  four 
horses  ?  four  teams  ? 

Name  four  things  you  like  to  do. 

Shut  your  eyes,  and  see  if  you  can  pick  out  four  blocks. 

Open  your  eyes  ;  how  many  have  you  ?     Try  again. 

Copy  the  word  four. 


20  FIRST   STEPS   IN   NUMBER. 

§  6.    Discoveries  in  Four. 

See  what  you  can  find  out  about  four  things. 

I  see  you  have  taken  one  away  from  your  four ;  how 
many  have  you  left  ? 

You  have  shown  me  four  minus  two ;  how  many  have 
you  left  ? 

How  many  have  you  taken  away  ?  how  many  are  left  ? 

Harry  has  shown  us  something.  All  put  your  blocks 
like  his.     (In  groups  of  two.) 

Mary  has  shown  us  something.  Put  your  blocks  like 
Mary's.     (In  groups  of  one  and  three.) 

Here  are  four  boxes.  You  may  see  if  you  can  use  them 
all  in  holding  your  blocks.  How  many  have  you  put  in 
each? 

Try  the  same  with  four  buttons ;  four  sticks ;  four  peb- 
bles ;  four  things  from  the  table. 

Show  me  something  else  about  four. 

§  7.    Facts  in  Four. 
Three  and  One. 

Take  three  blocks.  Take  one  more  block.  How  many 
blocks  have  you  ? 

Who  will  tell  me  a  story  about  this  ? 

Take  three  sticks.  Take  one  more  stick.  How  many 
sticks  have  you  ? 

Who  will  tell  me  a  story  about  this  ? 

Each  take  an  envelope.  Take  out  four  objects,  and 
think  of  a  story  for  three  things  and  one  more  thing. 
Who  is  ready  with  a  story  ? 

If  you  nod  your  head  three  times,  and  then  once,  how 
many  times  do  you  nod  your  head  ? 

If  you  have  three  cents  and  one  cent,  how  many  have 
you  in  all? 


THE  NUMBER  FOUR.  21 

You  may  tell  me  about  three  bugs  and  one  bug ;  three 
bicycles  and  one  bicycle. 

If  there  are  three  cows  in  a  pasture,  and  I  turn  in  an- 
other cow,  how  many  cows  in  the  pasture  then  ? 

If  there  are  three  street  cars  in  a  row,  and  another 
street  car  comes  up  to  them,  how  many  street  cars  are 
there  then? 

If  you  jump  three  feet,  and  then  jump  one  more  foot, 
how  many  feet  will  you  jump  in  all? 

If  you  bring  in  three  armfuls  of  wood  before  breakfast, 
and  one  after,  how  many  armfuls  of  wood  will  you  bring 
in  altogether  ? 

If  you  have  three  dresses  for  your  doll,  and  make  one 
more  dress,  how  many  dresses  will  she  then  have  ? 

You  may  tell  me  about  three  boys  and  one  boy ;  three 
books  and  one  book  ;  three  words  and  one  word ;  three 
clocks  and  one  clock ;  three  lamps  and  one  lamp. 

Exercise  for  Review. 

If  there  is  nothing  on  your  desk,  and  I  lay  one  block 
there,  how  many  things  will  there  be  on  your  desk  ? 

If  you  have  no  playthings,  and  I  give  you  a  ball  and  a 
top,  how  many  playthings  will  you  have? 

A  cat  is  playing  with  a  mouse ;  how  many  animals  arc 
there?  The  kitten  comes  to  join  the  fun;  how  many  arc 
there  now  ?  The  mouse  gets  away  and  slips  into  a  hole ; 
how  many  are  left  ?  The  kitten  runs  off  to  play ;  how 
many  are  left  ? 

A  dog  and  a  pup  come  into  the  room  together;  how 
many  animals? 

Here  is  a  couple  of  blocks  ;  how  many  blocks  ? 

Show  me  a  couple  of  spools;  a  couple  of  buttons;  a 
couple  of  pictures. 


22  FIRST   STEPS    IN   NUMBER. 

How  many  boots  does  it  take  to  make  a  pair  of  boots? 
how  many  mittens  to  make  a  pair  of  mittens  ? 

If  you  have  a  pair  of  boots  and  an  odd  boot,  how  many 
have  you  ? 

If  you  sell  the  odd  boot,  how  many  boots  will  you  have? 

If  you  wear  out  one  of  these  boots,  how  many  boots  will 
you  have  left? 

If  you  find  another  odd  boot,  how  many  boots  will  you 
have  ? 

In  a  stable  is  a  pair  of  horses  and  a  single  horse.  How 
many  horses  are  in  the  stable  ? 

If  the  owner  drives  out  with  the  pair,  and  his  daughter 
with  the  single  horse,  how  many  horses  will  be  left  in  the 
stable? 

If  there  are  four  mittens  on  the  radiator,  to  how  many 
little  boys  do  you  think  they  belong  ? 

If  four  stockings  are  hung  up  Christmas  Eve,  how  many 
children  will  be  up  bright  and  early  Christmas  morning  to 
see  what  is  in  the  stockings  ? 

If  Santa  Claus  brings  to  each  of  these  children  a  bag  of 
candy,  how  many  bags  will  he  bring  ? 

One  block  and  one  block  are  how  many  blocks  ? 

One  block  and  two  blocks  are  how  many  blocks  ? 

Three  blocks  and  one  block  are  how  many  blocks  ? 

Two  blocks  and  one  block  are  how  many  blocks  ? 

Two  blocks  minus  two  blocks  are  how  many  blocks  ? 

Three  blocks  minus  two  blocks  are  how  many  blocks  ? 

How  many  pairs  of  mittens  does  it  take  for  one  boy  ? 
how  many  mittens? 

How  many  pairs  of  boots  does  it  take  for  one  boy  ?  how 
many  boots  ? 

How  many  pairs  of  boots  does  it  take  for  Harry  and  Ned? 
how  many  pairs  of  stockings  ?  how  many  pairs  of  skates  ? 

You  may  write  the  word  one  on  your  slates. 


THE   NUMBER   FOUK.  23 

One  and  Three. 

Take  one  block.  Take  three  more  blocks.  How  many- 
blocks  are  one  block  and  three  more  blocks  ? 

Tell  me  a  story  about  one  shovel  and  three  more 
shovels,  Jamie;  about  one  fan  and  three  more  fans,  Annie; 
about  one  pail  and  three  pails,  Harry;  about  one  bell  and 
three  bells,  Alice  ;  about  one  drum  and  three  drums,  Joseph. 

(The  objects  referred  to  are  of  paper,  and  when  not  in  use  can  be 
neatly  packed  away  in  separate  envelopes.) 

One  chicken  and  three  chickens  are  how  many  chickens  ? 

One  kitten  and  three  kittens  are  how  many  kittens  ? 

One  boy  and  three  girls  are  how  many  children? 

Tell  me  a  story  about  one  dove  and  three  doves. 

Who  has  a  story  for  one  and  three  are  four  ?  another  ? 
another  ?  another  ? 

Four  minus  One. 

Put  one  of  your  four  blocks  under  the  table. 

How  many  have  you  left  ? 

Tell  me  a  story  about  four  blocks  minus  one  block ;  four 
books  minus  one  book ;  four  apples  minus  one  apple ;  four 
button-hooks  minus  one  button-hook;  four  knives  minus 
one  knife ;  four  boxes  minus  one  box. 

If  one  wheel  should  come  off  a  carriage,  how  many 
wheels  would  be  left  ? 

If  a  dog  hurts  one  of  his  legs,  on  how  many  legs  does  he 
walk  ? 

Exercise  for  Review. 

How  many  fingers  do  I  hold  up?  (Four.)  Now?  (Three.) 
Now?  (Two.) 

How  many  blocks  do  I  show  you  ?  (Four.)  How  many 
marks  on  the  board  ?  (Two.)  How  many  pieces  of  paper  ? 
(Three.) 


24  FIEST   STEPS    IN   NUMBEr.. 

(Teacher  shows  two  blocks  and  one  block.) 

How  many  here  ?     (Touching  two.) 

How  many  here  ?     (Touching  one.) 

Tell  me  what  you  see,  then. 

(I  see  two  blocks  and  one  block.) 

Who  sees  two  blocks  and  one  block  ? 

How  many  blocks  are  two  blocks  and  one  block  ? 

Eead,  then,  what  I  show  you. 

(Teacher  shows  a  group  of  two  and  a  single  block ;  then 
blowly  brings  the  two  groups  together,  while  the  child 
reads,  Two  blocks  and  one  block  are  three  blocks.) 

Eead  the  same  with  these  spools. 

(Two  spools  and  one  spool  are  three  spools.) 

With  these  buttons ;  with  these  cups. 

Read  what  I  show  3^ou  now. 

(Three  splints  and  one  splint  are  four  splints.) 

Now. 

(Three  boxes  and  one  box  are  four  boxes.) 

Now. 

(One  shell  and  one  shell  are  tv/o  shells.) 

These  exercises  are  very  important  in  training  the  eye  to  quick 
and  accurate  seeing. 


Four  minus  Three. 

Take  four  blocks. 

Put  three  of  your  four  blocks  under  the  table ;  how 
many  remain? 

If  I  have  four  plums,  and  eat  three  plums,  how  many 
plums  have  I  left  ? 

If  George  has  four  tops,  and  three  will  not  spin,  hov/ 
many  will  spin  ? 

If  there  are  four  pencils  on  the  table,  and  three  fall  off, 
how  many  remain  on  the  table  ? 


THE   NUMBER   FOUR.  25 

Four  boys  are  on  one  sled ;  three  get  tipped  off;  how 
many  remain  on  the  sled  ? 

Four  cards  are  on  a  shelf;  three  fall  off;  how  many 
remain  on  the  shelf? 

Make  four  marks  on  the  board ;  rub  out  three ;  how 
many  are  left  ? 

Four  postage  stamps  are  in  the  drawer ;  I  use  three ; 
how  many  are  left? 

If  you  have  four  cents,  and  buy  a  three-cent  postage 
stamp,  how  many  cents  have  you  left  ? 

Tell  me  a  story  about  four  minus  three. 


Exercise  for  Revie'w. 

Tell  me  a  story  about  four  minus  one ;  three  minus  one ; 
two  minus  one ;  one  minus  one  ;  three  minus  two ;  two 
minus  two ;  three  minus  three. 

Johnnie  has  three  words  written  on  his  slate,  and  Bennie 
two  ;  which  has  more  ?  how  many  more  ? 

Bennie  and  Ned  had  each  a  pair  of  mittens ;  Bennie  lost 
one  of  his  mittens  and  his  mother  knit  another  pair  for 
him  ;  which  had  the  more  mittens  then  ?  how  many  more  ? 

A  dog,  a  boy,  his  sled,  and  a  girl  on  the  sled,  are  how 
many  ? 

A  boy  left  his  coat  on  the  chair,  his  hat  on  the  table,  and 
his  book  on  the  floor ;  how  many  things  did  he  have  to 
pick  up  and  put  in  place  ? 

There  is  a  clock,  a  vase,  a  picture,  and  a  large  shell  on 
my  shelf;  I  remove  the  clock,  the  vase,  and  the  picture; 
how  many  things  remain  on  my  shelf?  I  put  back  the 
clock  and  the  vase ;  how  many  things  are  then  on  my 
shelf? 


26  FIRST  STEPS   IN   NUMBER. 

Two  and  Two. 

Take  two  blocks.  Take  two  more  blocks.  How  many 
are  two  blocks  and  two  blocks  ? 

You  may  choose  the  objects  that  you  wish  to  talk  about, 
and  tell  me  a  story  about  two  things  and  two  more  things. 

Your  two  hands  and  my  two  hands  are  how  many  hands  ? 

Your  mittens  and  my  mittens  are  how  many  mittens? 

You  may  call  your  blocks  tin  pails,  and  tell  me  a  story 
about  two  tin  pails  and  two  tin  pails ;  tell  me  about  two 
cows  and  two  cows;  two  cups  and  two  cups;  ^ two  forks 
and  two  forks;  two  chairs  and  two  chairs;  two  pins  and 
two  pins ;  two  pictures  and  two  pictures ;  two  bells  and 
two  bells ;  two  fans  and  two  fans. 

Take  a  couple  of  buttons  ;  take  two  more  buttons.  How 
many  buttons  have  you  ? 

One  boy  had  two  tops ;  another  had  two  balls.  How 
many  playthings  had  they  together  ? 

If  they  exchanged  a  ball  and  a  top,  how  many  playthings 
would  each  have  ? 

How  many  would  they  have  together  ? 

Here  is  a  cup  and  saucer,  and  here  is  a  cup  and  saucer ; 
how  many  cups  ?  how  many  saucers  ?  how  many  cups  and 
saucers  together  ? 

Four  minus  Two. 

Hold  up  four  fingers;  shut  down  two;  how  many  remain 
up? 

Show  me  four  buttons  ;  cover  up  two ;  how  many  re- 
main in  sight? 

Here  are  four  dogs ;  you  may  have  two ;  how  many 
have  I  ? 

Here  are  four  spoons  ;  we  will  put  two  away  ;  how  many 
remain  ? 


THE   NUMBER  FOUR.  27 

Show  me  four  blocks ;  take  two  away  ;  how  many  have 
you  ?     Tell  me  a  story  about  this  ;  another  ;  another. 

If  there  were  four  buttons  to  sew  on  your  boot,  and 
mamma  sews  on  two,  how  many  more  will  there  be  to  sew 
on? 

If  you  have  four  cents,  and  buy  a  two-cent  postage 
stamp,  how  many  cents  have  you  left  ? 

If  you  have  four  errands  to  do,  and  do  two  of  them,  how 
many  have  you  left  to  do? 

Exercise  for  Review. 

Show  me  three  splints ;  how  many  times  can  you  take 
one  away  before  they  are  all  gone  ? 

Show  me  two  splints ;  how  many  times  can  you  take  one 
away  before  they  are  all  gone  ? 

Four  boys  start  off  for  some  fun,  and  two^get  angry ;  how 
many  have  the  fun  ? 

Four  little  girls  have  a  party ;  two  play  with  dolls,  and 
the  rest  play  company.     How  many  play  company  ? 

Tell  me  two  things  they  talk  of. 

Tell  me  three  games  you  can  play. 

Dates,  figs,  raisins,  and  prunes;  how  many  kinds  of  fruit? 

Three  sparrows  are  taking  a  bath  in  a  fountain,  and  one 
sparrow  is  on  the  edge  of  the  fountain;  how  many  more 
sparrows  are  taking  a  bath  than  are  on  the  edge  of  the 
fountain  ? 

A  cat,  two  kittens,  and  a  mouse  are  how  many  animals  ? 
The  mouse  runs  away;  how  many  animals. are  left?  The 
cat  runs  after  the  mouse  ;  how  many  are  left  ?  One  kitten 
runs  off;  how  many  then  remain? 

What  is  left  when  three  cents  are  taken  from  four  cents  ? 
two  spools  from  four  spools?  one  button  from  four  buttons? 
three  oranges  from  three  oranges?  three  pies  from  four  pies? 


28  FIEST   STEPS   IN   NUMBER. 

Four  divided  by  Two. 

In  four  cents  how  many  two  cents  ? 

There  are  four  doves,  two  in  a  nest;  how  many  nests? 

There  are  four  stockings ;  how  many  pairs  ? 

I  have  four  mittens  ;  how  many  pairs  ? 

If  you  have  four  boots,  how  many  pairs  have  you  ? 

There  are  four  door-knobs,  two  on  a  door ;  how  many 
doors  ? 

If  there  are  four  kittens,  two  on  a  mat,  how  many  mats? 

I  see  four  blinds,  two  on  each  window ;  how  many  win- 
dows ? 

I  have  four  apples,  two  on  a  plate  ;  how  many  plates  ? 

There  are  four  children,  two  at  a  desk ;  how  many 
desks  ? 

I  have  four  cents  ;  how  many  apples  can  be  bought  at 
two  cents  apiece.? 

There  are  four  trunk-handles ;   how  many  trunks  ? 

I  have  four  sticks  of  candy,  and  give  them  to  two  chil- 
dren, giving  the  same  number  to  each ;  how  many  sticks 
does  each  child  receive  ? 

There  are  four  pillows,  two  on  a  bed ;  how  many  beds  ? 

Take  two  blocks  from  your  four  blocks  just  as  many 
times  as  you  can ;  how  many  twos  do  you  find  in  four  ? 

Exercise  for  Review. 

A  bookseller  had  four  rows  of  books  in  his  window ;  one 
row  tumbled  off;  how  many  rows  remained  ? 

He  then  took  down  two  more  rows ;  how  many  were  left? 

Afterward  he  put  back  the  three  rows  ;  how  many  rows 
were  there  then  ? 

Charley  gets  a  cent  for  every  paper  he  sells ;  how  many 
cents  will  he  get  for  selling  three  papers  ? 


THE   NUMBER  FOUR.  29 

Harry  has  four  cents ;  lie  spends  one  cent,  and  then  he 
earns  another ;  how  many  cents  has  he  ? 

Tom  has  two  cents  and  spends  one,  then  earns  one ;  how 
many  cents  has  he? 

Mary  has  four  cents  and  spends  two  cents,  and  then 
earns  two  more  ;  how  many  cents  has  she  ? 

If  Ed  had  one  cent  and  should  earn  three  more  cents,  and 
then  spend  three  cents,  how  many  cents  would  he  have  ? 

If  I  had  some  pencils  on  my  desk  and  should  give  you 
three,  then  get  three  from  the  library,  how  many  more 
pencils  would  I  have  on  my  desk  than  before  ?  If  I  gave 
you  four,  and  then  got  three  from  the  library,  how  many 
less  would  I  have  on  my  desk  ? 

If  you  have  some  money  and  spend  four  cents,  then  I 
give  you  two  cents,  have  you  more  or  less  money  than  at 
first  ?  If  you  spent  two  cents,  and  I  should  give  you  four, 
would  you  have  more  or  less  money  than  at  first  ? 

Two  Twos. 

Show  me  two  blocks ;  another  two  blocks. 

How  many  blocks  in  all  ? 

Here  are  two  buttons ;  take  two  more  buttons ;  how 
many  have  you  ? 

Show  me  two  paper  patterns ;  two  more ;  how  many 
paper  patterns  in  all  ? 

There  are  two  sleeves  to  one  dress ;  how  many  sleeves 
to  two  dresses? 

There  are  two  mittens  in  one  pair ;  how  many  in  two 
pairs  ? 

There  are  two  horses  in  one  span  ;  how  many  horses  in 
two  spans  ? 

There  are  two  covers  to  one  book ;  how  many  covers  to 
two  books  ? 


30  FIRST   STEPS   IN   NUMBER. 

If  there  are  two  bottles  to  one  inkstand,  how  many  bot- 
tles to  two  such  inkstands? 

There  are  two  blades  to  one  knife ;  how  many  to  two 
such  knives  ? 

How  many  hands  have  two  boys?  how  many  eyes?  how 
many  cheeks  ?  how  many  ears  ?  how  many  thumbs  ? 

How  many  boots  will  it  take  for  two  boys  ? 

How  many  pairs  of  boots  will  it  take  for  two  boys  ? 

Two  apples  cost  two  cents  each ;  how  many  cents  do  both 
cost  ? 

If  I  buy  two  pencils  at  two  cents  each,  how  many  cents 
do  I  pay  ? 

Two  pens  cost  two  cents  each  ;  how  many  cents  do  both 
cost? 

Two  books  cost  two  cents  each ;  what  do  both  cost  ? 

Exercise  for  Review. 

You  may  take  three  blocks  ;  arrange  them  all  the  ways 
you  can.  You  may  arrange  three  straight  lines  on  the 
board  all  the  ways  you  can  ;  three  dots  on  the  board. 

Point  in  three  directions. 

You  may  touch  each  one  of  three  blocks  and  say  ''one" 
each  time.     How  many  times  did  you  say  "one"? 

Do  the  same  with  two.  How  many  times  did  you  say 
"one "? 

Do  the  same  with  four.  How  many  times  did  you  say 
"one"? 

Four  minus  Four. 

Here  are  four  blocks  on  the  table ;  put  four  under  the 
table.     How  many  are  left  ? 

There  were  four  lamp  chimneys  ;  four  got  broken.  How 
many  whole  ones  are  left  ? 


THE   NUMBER  FOUR.  31 

There  were  four  apples  in  the  drawer ;  four  were  taken 
out  of  the  drawer.     How  many  were  left  in  the  drawer  ? 

There  were  four  poor  '^^'s  on  a  slate ;  the  teacher  rubbed 
out  four  poor  i's.     How  many  were  left  to  be  seen  ? 

There  are  four  books  to  cover  ;  I  cover  four.  How  many 
remain  to  be  covered  ? 

Four  men  were  in  the  post-office  ;  four  men  left  the  post- 
office.     How  many  men  were  in  the  post-office  then  ? 

Four  boys  were  turning  summersaults ;  the  recess-bell 
rang,  and  four  boys  went  into  school.  How  many  boys 
were  left  turning  summersaults  ? 

Four  girls  were  making  wreaths  ;  four  girls  went  in  to 
dinner.     How  many  were  left  making  wreaths  ? 

Four  divided  by  One. 

Here  are  four  cents ;  see  how  many  pictures  at  a  cent 
apiece  you  can  buy  of  George. 

See  how  many  tops  at  a  cent  apiece  you  can  buy ;  how 
many  pencils  at  a  cent  apiece ;  how  many  erasers  at  a  cent 
apiece  ;  how  many  sheets  of  paper  at  a  cent  a  sheet. 

I  have  four  apples.  To  how  many  children  can  I  give 
them  if  I  give  one  to  each  child  ? 

I  have  four  sponges  to  lend.  How  many  boys  can  I 
supply  with  sponges,  giving  one  to  each  ? 

Grace  has  four  more  stories  to  write  in  her  language 
book.  If  she  writes  one  a  day,  how  many  days  will  it  take 
to  finish  her  book  ? 

How  many  boys  will  four  hats  supply  ?    . 

Four  Ones. 

Here  are  four  cups,  each  with  a  handle.  How  many 
handles  in  all  ? 

Here  are  four  knives.     How  many  handles  ? 


32  FIRST  STEPS   IN   NUMBER. 

Here  are  four  saucers,  each  with  a  cup.  How  many 
cups  are  here  ? 

There  are  four  boys,  each  with  a  hat.  How  many  hats 
do  you  see  ? 

There  are  four  girls,  each  with  a  fan.  How  many  fans 
have  they  ? 

I  see  four  slates,  each  with  a  pencil.  How  many  pencils 
can  I  see? 

There  are  four  books,  with  a  book-mark  in  each.  How 
many  book-marks  in  all  ? 

There  are  four  tables,  each  with  a  cover.  How  many 
covers  does  it  take  ? 


§8.    Comparison  of  Four  with  Numbers  Known. 

I  have  four  cents,  Jamie  has  three.  Who  has  more  ? 
How  many  more  ? 

I  have  four  pencils,  Willie  has  three.  How  many  more 
have  I  ? 

One  hen  has  four  chickens  and  another  has  three ;  how 
many  more  has  the  one  than  the  other  ? 

One  man  walks  four  miles  an  hour,  another  three ;  how 
many  more  miles  does  the  first  walk  ? 

Tell  me  a  story  about  this  ;  another ;  another. 

How  many  more  legs  has  a  dog  than  you  ? 

A  chair  has  four  legs  and  two  rockers ;  how  many  more 
legs  than  rockers  has  the  chair  ? 

A  chair  has  one  seat  and  four  legs ;  how  many  more  legs 
than  seats? 

My  pencil  cost  two  cents,  my  rubber  four ;  how  many 
more  cents  did  my  rubber  cost  ? 

Four  books  are  how  many  more  than  three  books  ?  than 
one  book  ?  than  two  books  ? 


THE   NUMBER   FOUR.  33 

How  many  dots  have  I  shown  you  on  the  board  ?  Put 
enough  dots  with  it  to  make  four.  How  many  did  you  add 
to  make  four  ? 

How  many  dots  do  I  show  you  this  time  ?  Add  enough 
to  make  four.     How  many  did  you  add  ? 

Add  enough  dots  to  this  number  to  make  four  dots.  How 
many  did  you  add? 

Erase  enough  of  these  four  dots  to  leave  one  dot.  Of 
these  four  dots  to  leave  two.  Of  these  four  dots  to  leave 
three  dots. 

A  two-cent  coin  is  equal  in  value  to  how  many  one-cent 
coins  ?  Then  two  two-cent  coins  are  how  many  cents  more 
than  a  one-cent  coin?  how  many  cents  more  than  three 
one-cent  coins? 

One  doll  is  how  many  less  than  four  dolls  ?  Two  dolla 
are  how  many  less  than  four  dolls?  Three  dolls  are  how 
many  less  than  four  dolls  ? 

A  dog  has  four  legs  and  one  tail ;  how  many  more  legs 
has  he  than  tails  ? 

A  horse  requires  four  shoes,  and  a  boy  two ;  how  many 
less  does  the  boy  require  than  the  horse  ? 

A  lamb  has  four  legs,  two  eyes,  and  two  ears  ;  how  many 
more  legs  than  ears  ?  how  many  more  legs  than  eyes  ?  how 
many  more  legs  than  eyes  and  ears  together  ? 

Four  are  how  many  more  than  three?  than  two?  than 
one  ?  than  none  ? 

Three  are  how  many  less  than  four?  two  are  how  many 

less  than  four?  one  is  how  many  less  than  four? 

Copy : 

•  ••  •••  •••• 

one.  two.  three.  four. 


CHAPTEE   IV. 

THE    NUMBER    FIVE. 


§  9.   Five  as  a  Whole. 

Show  me  four  blocks ;  put  one  more  with  them.  You 
have  shown  me  five  blocks. 

Show  me  five  fingers ;  five  children  ;  five  marks  on  the 
board. 

Make  five  us  ;  five  i's. 

Show  me  five  words  on  the  board  that  you  know. 

Show  me  five  sticks ;  five  pencils ;  five  pieces  of  paper ; 
five  desks  ;  five  chairs. 

Bring  me  five  things  from  the  play  table;  five  things 
from  my  desk. 

Tell  me  where  you  have  seen  ^ve  men  ;  five  horses ;  five 
cars ;  five  birds. 

What  else  have  you  seen  five  of? 

Copy  the  word  five. 

§  10.    Discoveries  in  Five. 

Show  me  five  blocks. 

Put  your  blocks  as  I  put  mine. 

Who  can  put  his  some  other  way?  some  other  way? 
some  other  way  ? 

I  will  take  one  of  my  five  blocks  away.  You  may  do 
the  same. 

What  other  number  can  you  take  away  ?  what  other  ? 
what  other? 


THE   NUMBER   FIVE. 


35 


Exercise  for  Review. 

Tell  me  how  many  blocks  are  four  blocks  minus  one 
block.  (Teacher  performs  the  operation  with  the  blocks 
as  child  reads.) 

Three  blocks  minus  one  block. 

Two  blocks  minus  one  block. 

One  block  minus  one  block. 

Read  this.  (Teacher  shows  a  number  of  blocks  and 
takes  away  some  of  them.     Child  reads  as  above.) 

Eead  this.     (Four  minus  two  are  two.) 

Tell  me  the  number  of  dots  as  I  point. 


•  •  • 


•  • 

• 

• 

• 
• 

:• 

•: 

:•• 

••: 

•  • 

•  • 

•  •  •  • 

• 

• 
• 
• 

• 

• 
• 
• 

• 
• 
• 
• 

• 

•  • 
•     • 

•     • 

•  •  • 

• 

•  • 

•  • 

• 

•  • 

• 

• 

• 

• 

•  • 

• 

• 

•  •  • 

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36  FIRST  STEPS   IN   NUMBER. 

§  11.     Facts  in  Five. 
Four  and  One. 

Take  four  blocks.  Take  one  more  block.  How  many 
blocks  are  four  blocks  and  one  block  ? 

Make  four  marks  on  the  board.  Make  one  more  mark  on 
the  board.    How  many  marks  are  four  marks  and  one  mark  ? 

Find  four  bright  stars  on  my  chart.  Find  one  more 
star.     How  many  stars  have  you  found  ? 

Find  four  rings  and  one  ring.     How  many  rings? 

Show  me  four  blocks ;  one  more  block.  How  many 
have  you  in  all  ? 

Show  me  four  buttons  and  one  button.  How  many 
buttons  ? 

I  show  you  four  fingers  on  one  hand,  and  one  finger  on 
the  other.     How  many  fingers  ? 

I  have  four  bits  of  crayon  in  one  hand,  and  one  in  the 
other.     How  many  bits  of  crayon  in  all  ? 

If  I  have  four  blocks,  and  you  give  me  one  more,  how 
many  blocks  shall  I  have  ? 

Give  me  four  splints,  please ;  now  give  me  one  more. 
How  many  have  I  ? 

How  many  horses  are  four  horses  and  one  horse  ? 

How  many  cows  are  four  cows  and  one  cow  ? 

How  many  days  are  four  days  and  one  day  ? 

How  many  weeks  are  four  weeks  and  one  week  ? 

How  many  months  are  four  months  and  one  month  ? 

How  many  years  are  four  years  and  one  year  ? 

How  many  boys  are  four  boys  and  one  boy  ? 

I  see  four  stars  in  the  sky ;  one  more  shines  out.  How 
many  stars  can  I  see? 

Four  white  clouds  and  one  white  cloud  are  how  many 
clouds? 

Four  dogs  are  playing  in  the  street,  and  another  dog  is 
looking  on.     How  many  dogs  in  all? 


THE  NUMBER  FIVE.  37 


One  and  Four. 

Show  me  one  block ;  now  show  me  four  more.  How 
many  have  you  shown  me  ? 

One  block  and  four  more  blocks  are  how  many  blocks? 

Show  me  one  button  ;  show  me  four  more  buttons.  How 
many  buttons  ? 

Tell  me  a  story  about  one  and  four ;  another  ;  another. 

If  there  is  one  pig  in  the  pen,  and  four  more  are  put  in 
the  pen,  how  many  will  there  be  in  the  pen  ? 

One  boy  is  playing  foot-ball,  and  four  more  come  to  play 
with  him.     How  many  boys  are  then  playing  foot-ball  ? 

One  fly  is  in  the  room ;  four  more  get  in.  How  many 
flies  are  in  the  room  ? 

One  fly  is  in  a  spider's  web  ;  four  more  get  caught.  How 
many  flies  are  in  the  web  ? 

One  hat  was  on  the  rack ;  four  more  are  hung  with  it. 
How  many  hats  are  on  the  rack  ? 

One  little  boy  is  looking  out  of  the  window ;  four  more 
come  to  look  out.  How  many  are  looking  out  of  the 
window  ? 

Annie  finds  one  pin  one  day,  and  four  pins  the  next. 
How  many  pins  does  she  find  altogether  ? 


Five  minus  One. 

Show  me  five  blocks. 

Put  one  of  your  five  blocks  under  the  table. 
How  many  have  you  left  ? 
Tell  me  that  story. 

You  may  call  your  blocks  rabbits,  and  tell  me  that  story. 
Call  yours  dolls,  and  tell  me  a  story  like  this.    Who  will 
tell  me  another  ?  another  ?  another  ? 


38  FIRST  STEPS   IN   NUMBER. 

School  keeps  Monday,  Tuesday,  Wednesday,  Thursday, 
and  Friday  ;  five  days  in  the  week.  If  you  are  absent  one 
day,  how  many  days  do  you  come  ? 

There  are  five  fingers  on  one  hand,  with  the  thumb. 
How  many  without  the  thumb  ? 

You  had  five  is  on  your  slate  ;  I  rubbed  one  out.  How 
many  remained? 

Five  boys  play  ball ;  one  does  not  like  it,  and  goes  off. 
How  many  boys  are  left  ? 

Five  persons  are  at  a  table;  one  is  excused.  How  many 
remain  ? 

Five  boys  are  playing  fox  and  geese  ;  one  boy  is  the 
fox,  and  the  rest  are  geese.     How  many  are  geese  ? 

I  have  five  nuts,  but  one  is  bad.     How  many  are  good? 

There  are  five  teams  in  the  street,  and  one  moves  off. 
How  many  are  left  ? 

Five  boys  are  skating,  and  one  falls  down.  How  many 
go  on? 

There  are  five  biscuits  on  a  plate.  If  you  eat  one,  hov/ 
many  remain  ? 

Five  minus  Four. 

Show  me  five  blocks. 

Put  away  four. 

How  many  have  you  left? 

Tell  me  how  many  are  five  spools  minus  four  spools. 

There  were  five  eggs  in  the  basket ;  I  have  used  four. 
How  many  are  left  ? 

There  were  five  Noah's  Arks  in  the  shop  window,  and  a 
man  bought  four.     How  many  were  left? 

There  were  five  leaves  on  a  twig ;  four  blew  off.  How 
many  were  left  on  the  twig? 

Five  little  girls  are  reading ;  four  find  a  word  they  do 
not  know.     How  many  read  on  ? 


THE   NUMBER  FIVE.  39 

I  have  five  mittens;  four  are  alike.    How  many  are  odd? 

There  were  five  geranium  blossoms,  but  four  faded.  How 
many  were  left? 

If  I  have  five  postal  cards,  and  send  away  four,  how 
many  have  I  left  ? 

If  George  cuts  an  apple  into  five  pieces,  and  gives  away 
four,  how  many  has  he  left  ? 

Sarah  had  five  pieces  of  cake,  and  gave  four  pieces  to 
some  little  beggar  children.  How  many  pieces  had  she 
left? 

There  are  five  things  in  a  little  tray  on  the  table  :  a  pen- 
cil, a  rubber,  a  knife,  a  pen-holder,  and  a  paper-cutter.  If 
I  take  out  the  knife,  the  pencil,  the  rubber,  and  the  pen- 
holder, how  many  remain  ? 

Exercise  for  Review. 

Make  five  straight  up-and-down  lines  on  the  board.  Five 
right-and-left  lines.     Five  slanting  lines. 

You  may  name  the  days  of  the  week  that  you  come  to 
school.     How  many  days? 

Who  can  point  to  five  things  in  the  room  ?  to  five  figures 
on  the  clock  ? 

How  many  hands  on  the  clock  ? 

The  long  hand  goes  round  the  face  each  hour.  How 
many  times  will  it  go  round  in  two  hours  ?  in  three  hours  ? 
in  four  hours  ? 

Ned  goes  to  school  four  hours  in  the  day,  and  Jamie  one 
more  hour.     How  many  hours  does  Jamie  go  to  school  ? 

If  one  spool  of  cotton  costs  two  cents,  how  many  cents 
will  two  spools  of  cotton  cost  ? 

I  can  pick  two  quarts  of  berries  in  an  hour ;  how  many 
quarts  can  I  pick  in  two  hours  ? 

If  it  takes  me  an  hour  to  pick  two  quarts  of  berries,  how 
many  hours  will  it  take  to  pick  four  quarts  of  berries  ? 


40  FIRST   STEPS   IN   NUMBER. 

There  are  four  lamp-posts  on  the  street,  and  one  more  is 
put  up.  How  many  lamp-posts  are  there  ?  Show  me  this 
on  the  board,  by  drawing  the  lamp-posts. 

I  could  see  four  boats  on  the  water,  and  one  more  came 
in  sight.  Show  me  on  the  board  how  many  w^ere  in  sight 
then. 

Four  trees  were  in  front  of  our  house,  but  one  had  to  be 
cut  down.     Show  me  on  the  board  how  many  were  left. 

I  know  where  there  are  two  bird's  nests,  with  two  blue 
eggs  in  each  nest.  Show  me  how  many  eggs  there  are  in 
both  nests. 

At  the  table  this  noon  there  were  five  plates,  with  an 
apple  on  each  plate.  Show  me  this  on  the  board,  and  tell 
me  how  many  apples  there  were. 

Kead  what  I  show  you. 

Mary,  show  Nettie  something  to  read ;  show  Jennie 
something  to  read  ;  show  Cyrus  something  to  read. 

Annie,  show  Mary  something  to  read  ;  show  Cyrus  some- 
thing to  read. 

If  I  draw  one  tree  upright,  on  the  board,  and  four  lying 
down,  how  many  trees  do  I  draw  altogether  ? 

If  I  teach  four  classes  in  the  morning,  and  one  in  the 
afternoon,  how  many  classes  do  I  teach? 

There  were  three  funny  bonnets,  and  another  funny  bon- 
net came  to  join  them.     How  many  funny  bonnets  then  ? 

One  funny  bonnet  went  off  pouting.  How  many  funny 
bonnets  were  left? 

A  little  girl  was  under  each  funny  bonnet.  How  many 
little  girls  were  there  ? 

If  I  cut  one  apple  into  two  pieces,  and  then  another  into 
two  pieces,  how  many  pieces  have  I  ? 

If  I  give  two  pieces  away,  how  many  pieces  have  I  left? 

I  have  here  two  pieces  of  paper ;  I  will  cut  each  into 
two  equal  pieces.     How  many  equal  pieces  have  I  ? 


THE   NUMBER   FIVE.  41 

Show  me  a  couple  of  pieces.  Play  these  pieces  are 
ducks.  Show  me  a  pair  of  ducks.  Play  they  are  dollar 
gold  pieces.     Show  me  two  dollar  gold  pieces. 

Show  me  one  dollar  gold  piece,  and  three  dollar  gold 
pieces.     How  many  dollar  gold  pieces  ? 

Here  is  another  dollar  gold  piece.  Put  it  with  those  you 
have.     How  many  dollar  gold  pieces  have  you  now  ? 

I  have  a  stick  which  I  will  divide  into  four  equal  pieces. 
Show  me  two  of  the  equal  pieces.  How  many  more  equal 
pieces  are  there  ? 

Call  these  four  splints  silver  spoons.  Put  three  in  the 
spoon-holder,  and  tell  me  how  many  you  have  left. 

Take  one  of  the  spoons  from  the  spoon-holder,  and  tell 
me  how  many  will  remain  in  the  spoon-holder. 

Three  and  Two. 

Show  me  three  spools ;  put  two  more  with  them.  How 
many  spools  in  all  ? 

Give  me  three  buttons ;  now  give  me  two  more.  How 
many  have  I  ? 

Shut  your  hand ;  open  three  fingers ;  now  open  two 
more.     How  many  fingers  are  open  ? 

Here  are  three  knives  and  two  forks.  How  many  things 
are  here  ? 

Three  cups  and  two  saucers  stand  on  the  table.  How 
many  things  on  the  table  ? 

If  Nettie  comes  to  school  three  days  and  two  days  in  the 
week,  how  many  days  does  she  come  to  school? 

If  there  are  three  slices  of  bread  on  one  plate,  and  two 
on  another,  how  many  on  both  plates  ? 

There  are  three  little  kittens  in  the  basket,  and  two  on 
the  floor.     How  many  kittens  in  all  ? 

Three  cents  and  two  cents  are  how  many  cents  ? 


42  FIRST   STEPS   IN   NUMBER. 

A  three-cent  stamp  and  a  two-cent  stamp  cost  how  much? 
a  three-cent  j)en  and  a  two-cent  pen?  a  three-cent  ticket 
and  a  two-cent  ticket  ?  a  three-cent  paper  and  a  two-cent 
paper  ? 

It  costs  me  three  dollars  to  go  to  Nashua,  and  two  dol- 
lars from  Nashua  home.  How  many  dollars  is  my  fare 
home? 

Ned  learns  three  words  in  the  morning,  and  two  in  the 
afternoon.     How  many  words  does  he  learn  ? 

Who  can  tell  me  a  story  about  three  soap-bubbles  and 
two  soap-bubbles  ?  three  honey-bees  and  two  honey-bees  ? 
three  boats  sailing  down  the  river  and  two  boats  sailing  up 
the  river  ? 

Two  and  Three. 

This  knife  has  two  blades,  and  this  has  three ;  how  many 
blades  have  both  knives  together  ? 

Here  are  tw^o  pebbles  in  this  hand,  and  three  in  this  ; 
how  many  in  both  hands  together? 

I  make  two  dots ;  now  I  make  three  more.  How  many 
dots  have  I  made? 

If  you  make  two  us  on  the  board,  and  then  make  three 
more,  how  many  21  b  will  you  make? 

Show  me  that  two  sticks  and  three  sticks  are  five  sticks ; 
that  two  pencils  and  three  pencils  are  five  pencils ;  that 
two  fingers  and  three  fingers  are  five  fingers;  that  two 
boys  and  three  girls  are  five  children. 

Five  minus  Two. 

Show  me  five  blocks ;  take  away  two  blocks.  How  many 
blocks  remain  ? 

Tell  me  that  story. 

Show  me  five  splints ;  put  back  two  of  the  splints.  How 
many  splints  have  vou  now  ? 


THE   NUMBER   FIVE.  43 

Call  your  splints  men,  and  tell  me  that  there  were  five 
men,  and  that  two  walked  away. 

Call  them  lamp-posts,  and  tell  me  that  two  had  no  lamps 
on  them. 

Call  them  chimneys  which  a  man  had  to  build,  and  tell 
me  that  he  has  built  two. 

Call  them  slate  pencils,  two  of  which  got  broken. 

Call  them  curtain  sticks,  two  of  which  were  used  for 
curtains. 

Johnny  made  fiye  ^'s  on  his  slate ;  two  had  straight  lines, 
the  rest  did  not.     How  many  did  not  ? 

George  had  five  apples,  and  gave  two  of  them  to  his 
little  brother.     How  many  apples  had  he  left  ? 

There  are  five  school  days  in  a  week.  If  it  is  so  stormy 
that  Annie  is  absent  two  days,  how  many  days  does  she 
come? 

A  geranium  blossom  has  five  petals.  If  two  petals  fall 
off",  how  many  remain  on  the  blossom  ? 

A  pansy  blossom  has  five  petals.  If  two  are  black  and 
the  rest  bright,  how  many  petals  are  bright  ? 

A  lady  had  a  calla  lily  with  five  blossoms  on  it.  She  cut 
off  two  of  the  blossoms.     How  many  remained  on  the  lily  ? 

A  man  had  five  horses ;  two  were  always  used  in  a  span. 
How  many  beside  the  span  did  he  have  ? 

There  were  five  peas  in  a  pod.  When  the  pod  was 
opened,  one  flew  up  in  the  air  and  one  fell  on  the  floor;  the 
rest  went  into  the  pan.     How  many  went  into  the  pan  ? 

-  Five  little  girls  were  running  in  a  line.  One  got  snapped 
ofif,  and  another  fell  down.  How  many  were  left  in  the 
line? 

Five  boys  were  playing  fox  and  geese.  One  boy  was  the 
fox,  and  one  goose  got  caught  before  he  could  hide.  How 
many  geese  remained  to  be  caught  ? 

Who  has  a  story  to  tell  me  for  five  minus  two  ? 


44  FIRST  STEPS   IN   NUMBER. 


Five  minus  Three. 

How  many  dots  do  I  show  you  on  the  board  ?  (Five.) 
You  may  rub  out  three  dots.  How  many  dots  are  left? 
Five  dots  minus  three  dots  are  how  many  dots  ? 

Here  are  five  lines ;  you  may  cross  out  three  lines.  How 
many  lines  are  not  crossed  ? 

There  are  five  erasers  at  that  board  ;  you  may  bring 
three  of  them  to  this  board.  How  many  remain  at  that 
board  ? 

Five  children  may  stand  in  a  row  ;  three  may  walk  off. 
How  many  are  left  in  the  row  ? 

Show  me  five  fingers  on  one  hand ;  shut  down  three. 
How  many  remain  open  ? 

Here  is  a  step-ladder  with  five  steps.  When  I  have 
mounted  three  steps,  how  many  more  steps  will  there  be  to 
mount  ? 

Here  are  five  pencils;  distribute  three  of  them  to  the 
children.     How  many  have  you  left  ? 

Each  take  five  blocks ;  put  three  of  them  behind  you. 
How  many  remain  on  the  table  ? 

Tell  me  a  story  for  that. 

Tell  me  a  story  for  five  feet  of  snow,  three  feet  of  which 
melted  away. 

You  are  in  school  five  hours  a  day.  If  three  are  in  the 
morning,  how  many  are  in  the  afternoon  ? 

If  you  have  five  lines  of  ns  to  make,  and  have  made 
three,  how  many  more  lines  of  n's  must  you  make  ? 

If  you  have  five  words  to  write,  and  write  three,  how 
many  more  words  have  you  to  write  ? 

If  you  have  five  cents,  and  buy  a  book  for  one  cent,  two 
pencils  for  a  cent,  and  ten  sheets  of  paper  for  a  cent,  how 
many  cents  have  you  left  ? 


THE   NUMBER   FIVE.  45 

If  I  buy  a  three-cent  postage  stamp,  and  give  five  cents 
in  payment,  how  much  change  ought  I  to  receive  ? 

I  have  a  pail  which  holds  five  pints  of  milk ;  there  are 
three  pints  of  milk  in  it.     How  much  more  will  it  hold  ? 

Here  are  five  marks  on  the  board,  which  you  may  call 
boys.  One  boy  turned  down  Depot  Street,  another  went 
up  Pleasant  Street,  and  one  went  into  the  post  office ;  the 
rest  walked  along  together.  How  many  walked  along 
together  ? 

Exercise  for  Review. 

How  many  sides  has  this  triangle  ?  /\ 

How  many  corners  has  this  triangle  ?  ^ — A 

How  many  sides  has  this  square  ?  I        1 

How  many  sides  has  this  blackboard  ?  I | 

How  many  corners  has  this  blackboard  ? 

Make  a  square  with  blocks,  putting  one  block  on  a  side. 
How  many  blocks  does  it  take  ? 

Put  a  bean  in  each  corner  of  this  square.  How  many 
beans  does  it  take  ? 

Make  a  triangle,  putting  a  block  on  each  side.  How 
many  blocks  does  it  take  ? 

Put  a  button  in  each  corner  of  the  triangle.  How  many 
buttons  does  it  take  ? 

How  many  corners  has  this  table  ? 

How  many  sides  has  this  table? 

How  many  legs  has  a  piano  ? 

How  many  stands  has  a  piano-stool? 

If  there  are  four  piano-stools,  how  many  stands  are  there  ? 

There  are  two  ends  to  your  desk,  and  a  front  side,  a 
back  side,  and  a  top.     How  many  parts  to  your  desk  ? 

Who  will  show  me  five  things  ? 

Who  will  show  me  four  things  ? 

Who  will  show  me  three  things  ? 


46  riEST   STEPS   IN   NUMBER. 

Kead  what  I  show  you.  (Teacher  shows  child  any 
operation  in  Addition  or  Subtraction  that  he  has  seen. 
Pupil  reads  as  teacher  makes  the  changes.) 

Show  me  that  three  spools  and  two  spools  are  five 
spools  ;  that  two  spools  and  three  spools  are  five  spools ; 
that  four  spools  and  one  spool  are  five  spools ;  that  one 
spool  and  four  spools  are  five  spools. 

One  minus  one  is  how  many  ? 

Two  minus  one  are  how  many  ? 

Three  minus  one  are  how  many  ? 

Four  minus  one  are  how  many  ? 

Five  minus  one  are  how  many  ? 

Two  minus  two  are  how  many  ? 

Three  minus  two  are  how  many  ? 

Four  minus  two  are  how  many  ? 

Five  minus  two  are  how  many  ?  •* 

Five  minus   Five. 

How  many  blocks  have  I  ?     (Five.) 

Tell  me  how  many  I  have  taken  away.  (Teacher  puts 
five  under  the  table.) 

How  many  have  I  left? 

You  may  show  me  that,  and  tell  me  about  it. 

Some  one  else  show  me  that  five  minus  five  leaves  none. 

You  may  each  call  your  blocks  fruit,  and  tell  me  about 
five  minus  five.  Call  them  animals.  Call  them  dishes. 
Call  them  chairs. 

Here  are  five  kittens ;  five  are  asleep.  How  many  are 
awake  ? 

There  were  five  horse-cars  in  the  street ;  five  were  mov- 
ing.    How  many  were  still  ? 

If  I  have  five  pencils  in  my  box,  and  take  out  five,  how 
many  are  left  ? 


THE  NUMBER  FIVE.  47 

Exercise  for  Review. 

Arrange  your  blocks  on  the  table  just  as  I  arrange  these 
dots  on  the  board.       • 

One  dot  at  each  corner  and  one  dot  in  the  middle  make 
how  many  dots  ? 

Like  this.     ^©^  How  many  have  you  ? 

Like  this.     ^^^  Like  this.      ^^ 

One  dot  in  the  upper  row  and  three  dots  in  the  lower 
row  make  how  many  dots  ? 

Three  dots  in  the  upper  row  and  two  dots  in  the  lower 
row  make  how  many  dots? 

Like  this.       •  •       How  many  did  I  make  this  time  ? 

If  you  have  two  weeks'  vacation  in  the  fall,  and  three  in 
the  winter,  how  many  weeks'  vacation  does  that  make  ?  If 
you  visit  three  weeks,  how  many  weeks  do  you  stay  at 
home? 

A  knife,  a  string,  a  bit  of  crayon,  a  cent,  and  a  nail  were 
found  in  Ned's  pocket.  How  many  things  ?  He  gave  the 
crayon  to  me,  spent  his  cent,  drove  his  nail  into  a  board, 
and  lost  his  knife.     How  many  things  remained  ? 

Five  divided  by  One. 

Here  are  five  dolls ;  give  one  to  each  little  girl.  To  how 
many  little  girls  can  you  give  them? 

Here  are  five  cents ;  put  each  in  a  box  by  itself.  How 
many  boxes  does  it  take  ? 

Here  are  five  crayons;  put  each  at  a  board  by  itself. 
How  many  boards  does  it  take  ? 

Here  are  five  paper  rings  ;  put  each  or  a  finger  by  itself. 
How  many  fingers  does  it  take  for  the  ^ve  rings  ? 

Here  are  five  cards ;  put  each  in  an  envelope  by  itself. 
How  many  envelopes  will  it  take  ? 


48  FIRST  STEPS   IN  NUMBER. 

If  a  housekeeper  had  ^ve  eggs,  and  used  one  a  day,  how 
many  days  would  the  five  eggs  last  her  ? 

If  a  family  used  a  pound  of  butter  a  day  on  the  table,  in 
how  many  days  would  they  use  five  pounds  ? 

Jamie  has  f^ye  cents ;  he  earned  a  cent  a  day.  How 
many  days  did  it  take  him  to  earn  the  five  cents  ? 

Five  Ones. 

Show  me  five  blocks,  with  a  button  on  each  block.  How 
many  buttons  are  there  ? 

Show  me  ^ve  boxes,  with  a  shell  in  each  box.  How 
many  shells  do  you  show  me  ? 

Here  are  five  boys;  each  may  take  one  block.  How 
many  blocks  have  the  boys  together  ? 

Show  me  five  tin  plates,  with  a  paper  cent  in  each  plate. 
How  many  cents  have  you  shown  me  ? 

Show  me  a  cup  in  each  plate.     How  many  cups? 

Five  boys  have  each  a  slate.  How  many  slates  do  they 
all  have  together  ? 

If  each  of  the  five  slates  has  a  sponge  fastened  to  it,  how 
many  sponges  have  all  the  slates  ? 

If  each  of  the  five  slates  has  a  pencil  on  it,  how  many 
pencils  have  all  the  slates  ? 

If  each  pencil  cost  a  cent,  how  many  cents  did  the  five 
pencils  cost  ? 

If  five  books  cost  each  a  cent,  how  many  cents  do  the 
books  cost? 

Five  boys  bought  each  a  sled.  How  many  sleds  did  all 
buy  together? 

I  have  five  little  nephews,  to  whom  I  give  a  Christmas 
present  apiece.     How  many  presents  must  I  buy  ? 

If  each  hangs  up  his  stocking  Christmas  Eve,  how  many 
stockings  will  be  hung  up  ? 


THE   NUMBER  FIVE.  49 


Exercise  for  Review. 

Put  on  the  board  marks  for  wliat  I  show  you.  (Teacher 
shows  different  combinations  of  numbers.  Child  shows  the 
same  combination  with  marks  on  the  board.  Teacher  shows 
a  number  and  subtracts  from  it.  Child  shows  the  number 
on  the  board  and  crosses  out  the  number  subtracted.) 

Read  what  you  have  shown  me  on  the  board. 

Illustrate,  with  marks  on  the  board,  the  stories  I  tell  you: 

Three  men  were  raking  hay  ;  two  more  men  went  to  rake 
hay  with  them. 

Three  hens  roosted  in  a  tree,  and  two  on  a  fence. 

I  have  three  plants,  with  a  blossom  on  each  plant. 

I  have  three  baskets,  with  two  handles  on  one,  and  one 
handle  on  each  of  the  others. 

I  have  three  cents  in  one  hand,  and  one  cent  in  the 
other  hand. 

James  put  five  eggs  in  his  pocket,  and  two  broke. 

There  were  ^ve  Christmas  trees  in  a  ring,  and  a  beauti- 
ful light  on  the  top  of  each  tree. 

I  can  see  five  houses,  with  a  chimney  on  each  house. 

I  have  at  home  a  cat,  two  kittens,  a  dog,  and  a  bird. 

Three  boats  are  going  up  river,  with  a  man  in  each  boat. 

Four  frogs  are  croaking  in  a  pond. 

Ed  has  two  rabbits,  two  squirrels,  and  a  parrot. 

Take  this  paper  money.  Johnny  may  be  the  salesman. 
The  others  may  be  his  customers  and  buy  these  things  that 
are  on  the  table. 

Nettie  may  be  the  first  customer. 

''  How  do  you  sell  your  apples?  " 

"I  sell  them  at  two  cents  apiece." 

'*I  will  take  two."  (Nettie  passes  a  five-cent  piece  in 
payment.) 


50  FIRST  STEPS   IN   NUMBER. 

"Two  apples  at  two  cents  apiece,  four  cents,  and  one 
cent  are  five  cents." 

Maggie  may  be  the  second  customer. 

"I  wish  for  a  spool  of  white  thread." 

"What  number  do  you  wish?  " 

"Number  60." 

"It  is  four  cents." 

(Maggie  passes  a  five-cent  piece  in  payment.) 

"One  spool  of  thread,  four  cents,  and  one  cent  are  five 
cents." 

Mary  may  buy  this  time. 

"I  wish  for  five  of  these  pictures." 

"These  pictures  are  a  cent  each." 

(Mary  counts  out  her  five  cents  and  passes  it  to  the  shop- 
keeper.) 

Mabel  may  buy. 

"I  will  take  three  one-cent  pencils."  (She  gives  two 
two-cent  pieces  in  payment.) 

"  Three  pencils  at  a  cent  apiece,  three  cents,  and  one 
cent  are  four  cents." 

§  12.   Comparison  of  Five  with  Numbers  known. 

Show  me  one  block.  ^ 

Show  me  two  blocks  beneath  this.  o     o 

Show  me  three  blocks  beneath  these.  o     o     o 

Show  me  four  blocks  beneath  these.  o     o     o     o 

Show  me  five  blocks  beneath  these.  o     o     o     o     o 

Which  is  the  smallest  number  ? 
Which  is  the  largest  number  ? 
Which  is  one  more  than  one? 
Which  is  one  less  than  five? 
Wliich  is  one  more  than  two  ? 
Which  is  one  less  than  four  ? 


THE   NUMBER   FIVE.  51 

Which  is  one  more  than  three  ? 

Which  is  one  less  than  three  ? 

Which  is  one  more  than  four  ? 

Which  is  one  less  than  two  ? 

Five  is  how  many  more  than  four  ? 

Five  is  how  many  more  than  three  ? 

Five  is  how  many  more  than  two  ? 

Five  is  how  many  more  than  one  ? 

Five  is  how  many  more  than  none  ? 

Four  and  how  many  are  five? 

Three  and  how  many  are  five  ? 

Two  and  how  many  are  five  ? 

One  and  how  many  are  five  ? 

Five  minus  one  are  how  many  ? 

Five  minus  two  are  how  many  ? 

Five  minus  three  are  how  many  ? 

Five  minus  four  are  how  many  ? 

Five  minus  five  are  how  many  ? 

Jamie  has  five  buttons  on  his  jacket,  and  Harry  has  four. 
Which  has  more  ?     How  many  more  ? 

I  have  two  two-cent  pieces,  and  a  five-cent  piece.  Which 
is  worth  the  more  ?     How  much  more  ? 

Nellie  has  copied  her  words  twice,  and  she  has  to  copy 
them  five  times.  How  many  more  times  must  she  copy 
them  ? 

I  have  five  letters  to  answer.  If  I  answer  three,  how 
many  more  have  I  to  answer  ? 

Jennie  has  five  handkerchiefs  to  hem.  If  she  hems  four, 
how  many  more  has  she  to  hem  ? 

Harry  has  a  five-cent  piece ;  Tom  has  a  one-cent  piece 

and  a  two-cent  piece.     How  much  more  money  has  Harry 

than  Tom  ? 

Copy : 

•         ••         •••         ••••         ••••• 

one.       two.       three.  four.  five. 


52  FIEST  STEPS   IN   NUMBER. 


§  13.   One-half. 


What  have  I  ?     (An  apple.) 

I  will  give  you  part  of  my  apple.  I  will  give  Mamie  the 
other  part. 

Look  at  the  two  pieces  into  which  I  cut  the  apple.  Which 
is  the  larger  piece?  (The  answer,  "They  are  just  the 
same,"  is  usually  given.  Give  the  word  "equal"  for  "just 
the  same.") 

What  have  I  now  ?     (A  card.) 

I  will  give  Ned  a  part  of  this  card.  I  will  give  Annie 
the  other  part. 

Look  at  the  two  pieces  into  which  I  have  cut  the  card. 
Which  is  the  larger  piece  ?     (They  are  equal.) 

You  may  cut  this  apple  into  two  equal  pieces. 

You  may  cut  this  paper  ring  into  two  equal  pieces. 

You  may  cut  these  paper  scissors  into  two  equal  pieces. 

You  may  divide  this  envelope  into  two  equal  pieces. 

You  may  divide  this  square  into  two  equal  pieces. 

Show  me  the  two  pieces  into  which  you  cut  the  apple. 
What  part  of  the  apple  is  each  piece  ? 

Each  of  the  pieces  is  one-half  of  the  apple. 

Show  me  one-half  of  the  apple. 

Show  me  the  other  half  of  the  apple. 

Show  me  the  two  pieces  into  which  you  cut  the  paper 
ring.     Which  is  the  larger  piece  ? 

Show  me  one-half  of  the  ring. 

Show  me  the  other  half  of  the  ring. 

Into  how  many  pieces '  did  you  cut  the  paper  scissors  ? 
Are  the  pieces  equal  ? 

Show  me  one  of  the  two  equal  pieces.  Can  you  tell  me 
what  part  of  the  scissors  it  is  ?  Show  me  the  other  half  of 
the  scissors. 


THE  NUMBER  FIVE.  53 

Show  me  one-half  of  the  envelope. 

Show  me  one-half  of  the  square. 

Ned,  you  may  give  Susie  half  of  this  apple,  and  keep  the 
other  half  yourself. 

Look  at  the  two  halves  of  the  apple.    Which  is  the  larger? 

I  will  divide  this  apple  into  halves.  Into  how  many 
parts  do  I  divide  it  ? 

What  part  of  the  apple  is  this?     (Holding  up  one  half.) 

What  part  of  the  apple  is  this  ?  (Holding  up  the  other 
half.) 

Show  me  half  of  an  apple. 

Show  me  another  half  of  an  apple. 

Show  me  half  of  this  sheet  of  paper ;  half  of  this  ring ; 
half  of  this  circle  ;  half  of  this  string. 

Draw  a  line  so  as  to  divide  your  slate  into  two  equal 
parts.  What  part  of  your  slate  is  one  part?  is  the  other 
part  ?  is  each  part  ? 

Here  is  a  square  on  the  board.  Draw  a  line  so  as  to 
divide  it  into  two  equal  parts.  What  part  of  the  square  is 
each  part  ? 

Show  me  what  you  think  to  be  half  of  this  stick  ;  half  of 
this  block ;  half  of  this  pencil ;  half  of  this  table ;  half  of 
this  line  ;  half  of  the  window ;  half  of  this  blind  ;  half  of 
this  radiator. 

Here  are  two  blocks.  Put  them  into  two  groups,  and 
have  just  as  many  in  one  group  as  in  the  other.  How  many 
in  each  group  ?     (One.) 

One  block  is  one-half  of  two  blocks. 

Show  me  one-half  of  two  blocks. 

One-half  of  these  two  sticks  is  how  many  sticks  ? 

One-half  of  these  two  buttons  is  how  many  buttons  ? 

One-half  of  these  two  pencils  is  how  many  pencils  ? 

Cyrus  had  two  cents.  He  gave  half  of  what  he  had  to 
me.     How  many  cents  did  he  give  me  ? 


54  FIRST  STEPS   IN  NUMBER. 

Here  are  four  blocks.  Put  them  into  two  equal  groups. 
How  many  in  each  group  ? 

Two  is  one-half  of  four. 

Show  me  one-half  of  four  blocks.  How  many  blocks  in 
one-half  of  four  blocks  ? 

Show  me  one-half  of  four  buttons.     How  many  buttons  ? 

Show  me  one-half  of  four  sticks.     How  many  sticks  ? 

If  I  have  four  apples,  and  give  you  half  of  what  I  have, 
how  many  shall  I  give  you  ? 

If  I  give  you  half  of  my  four  cards,  how  many  cards 
shall  I  give  you  ? 

If  I  have  four  weeks'  vacation,  and  spend  half  of  it  here, 
how  many  weeks  shall  I  stay  here  ? 

If  I  spend  the  other  half  of  it  at  home,  how  many  weeks 
shall  I  spend  at  home  ? 

Take  two  blocks,  and  separate  them  into  two  equal  parts. 
How  many  in  each  part  ? 

Take  four  blocks,  and  separate  them  into  two  equal  parts. 
How  many  in  each  part?  What  part  of  four  blocks  are 
two  blocks  ? 

This  is  one-half  an  apple.  How  many  such  parts  make 
a  whole  apple  ? 

Here  is  half  a  sheet  of  paper.  How  many  such  pieces  of 
paper  make  a  whole  sheet  of  paper  ? 

Here  is  a  half-pound  weight.  How  many  such  weights 
make  a  pound? 

Baby  drinks  a  half-pint  of  milk  every  morning.  How 
many  mornings  will  it  take  to  drink  a  pint  ? 

A  pint  is  half  of  a  quart.  How  many  pints  does  it  take 
to  make  a  quart  ? 

How  many  halves  of  an  apple  make  a  whole  apple  ? 

How  many  halves  of  an  orange  make  a  whole  orange  ? 

How  many  halves  of  an  hour  make  a  whole  hour  ? 

How  many  halves  of  a  pencil  make  a  whole  pencil  ? 


CHAPTER   V. 

THE    NUMBER    SIX. 


§  14.   Six  as  a  Whole. 

Show  me  five  blocks.  Show  me  one  more  block.  You 
have  shown  me  six  blocks. 

Show  me  six  fingers;  six  children;  six  marks  on  the 
board  ;  six  desks  ;  six  rounds  on  the  settee. 

Find  a  card  with  six  dots  on  it. 

Find  six  cents ;  six  buttons  ;  six  bits  of  crayon. 

Make  a  pen  and  put  six  pigs  in  it. 

Here  is  a  hen  on  the  board.  She  has  six  chickens.  Make 
dots  on  the  board  for  the  chickens. 

Here  is  a  block  of  houses.  It  has  six  chimneys.  Make 
a  straight  line  for  each  chimney. 

Where  have  you  seen  six  things  ? 

Name  six  things  you  have  seen  at  home,  and  take  a  block 
for  each  thing. 

Name  six  things  you  have  seen  in  the  shop  window ;  on 
the  street. 

Name  six  days  in  the  week ;  six  months  in  the  year. 

Who  is  six  years  old  ? 

Two  boys  may  stand  here,  back  to  back.  Each  walk 
straight  ahead  over  three  boards.  How  many  boards  apart 
are  you? 

Stand  in  the  same  way  again.  Each  boy  pass  three 
desks  and  stop.     How  many  desks  are  between  you  ? 

Copy  the  word  six. 


56  FIRST  STEPS   IN   NUMBER. 

§  15.    Discoveries  in  Six. 

Look  at  your  six  blocks. 

Who  can  find  out  something  about  six  ? 

What  has  Jennie  found  ?      (Two  threes  in  six.) 

Bennie  ?     (Three  twos  in  six.) 

Ned?     (Five  and  one  are  six.) 

Harry  ?     (Three  taken  from  six  leave  three.) 

Mary  ?     (Six  taken  from  six  leave  none.) 

Four  and  how  many  are  six  ? 

Two  and  how  many  are  six  ? 

One  and  how  many  are  six  ? 

Let  me  see  what  you  can  take  away  when  yov  have  six 
things. 

Call  them  geese,  and  let  a  fox  catch  some  of  them. 

Johnny,  how  many  has  he  caught  of  yours  ?  How  many 
have  you  left? 

How  many  has  he  caught  of  yours,  Mary,  and  how  many 
have  you  left  ?  Ned  ?  Bennie  ?  Jennie  ? 

Who  can  tell  me  a  story  about  six  ?  another  ? 

Exercise  for  Review. 

If  a  boy  stands  at  each  door  in  this  room,  how  many  boys 
will  you  see  standing  at  doors  ? 

If. I  tell  John  to  lower  half  the  windows  in  this  room, 
how  many  windows  will  he  lower  ? 

If  I  have  three  pencils  and  break  one,  then  buy  two  and 
give  one  away,  then  lose  one,  how  many  shall  I  have  ? 

If  I  take  three  steps  forward,  and  then  come  back  two 
steps,  then  go  on  three  steps,  how  many  steps  away  am  I 
from  where  I  started  ? 

If  you  get  three  Christmas  cards  in  the  mail,  and  two  in 
your  stocking,  how  many  cards  will  you  receive  in  all  ? 


THE   NUMBER  SIX.  57 

If  I  buy  a  dozen  Christmas  cards  at  one  store,  and  two 
dozen  at  another  store,  how  many  dozen  do  I  buy  in  all  ? 

If  it  takes  a  two-cent  stamp  to  send  one  Christmas  card, 
how  many  stamps  will  it  require  to  send  two  such  cards  ? 
How  many  cents  will  it  cost  to  buy  the  two  stamps  ? 

If  you  have  two  holidays  in  the  fall  term,  and  two  in 
the  spring  term,  how  many  holidays  will  you  have  in  both 
terms  ? 

Show  me  a  half  of  six  ;  a  half  of  four  ;  a  half  of  two ;  a 
half  of  this  square  ;  a  half  of  this  rectangle  ;  a  half  of  this 
piece  of  twine ;  a  half  of  your  forefinger ;  a  half  of  your 
arm  ;  a  half  of  your  face  ;  a  half  of  this  table. 

If  you  separate  these  four  blocks  into  two  equal  groups, 
how  many  blocks  will  there  be  in  each  group  ? 

What  part  of  four  blocks  are  these  two  blocks  ? 

What  part  of  four  pencils  are  these  two  pencils  ? 

What  part  of  four  cups  are  these  two  cups  ? 

If  you  must  put  away  your  boots,  hang  up  your  cap,  and 
brush  your  hair  before  supper,  how  many  things  have  you 
to  do? 

A  milkman  had  to  go  a  mile  and  a  half  to  the  pasture  to 
milk  his  cows,  and  back  again,  in  the  morning.  How  many 
miles  did  he  have  to  go  in  all  ? 

A  man  has  a  garden  to  dig,  which  will  take  him  four 
days ;  but  he  hires  a  man  to  help  him.  How  many  days 
will  it  take  both  together  to  dig  the  garden  ? 

How  many  rows  of  teeth  have  you  ?  How  many  fingers 
on  one  hand  ? 

Tell  me  a  story  about  four  minus  three ;  ^yq  minus  three ; 
three  minus  three ;  three  and  two ;  two  and  two ;  five  minus 
four. 

Who  can  tell  how  many  blocks  I  show  you  ?  how  many 
now?  how  many  now?  how^  many  now?  Show  me  four 
blocks  ;  five  blocks ;  three  blocks. 


58  FIKST  STEPS   IN   NUMBER. 

§  16.   Facts  in  Six. 
Five  and  One. 

Take  five  blocks.  Take  one  more  block.  How  many 
blocks  are  five  blocks  and  one  more  block  ? 

Ella  may  take  five  pink  shells.  She  may  put  one  more 
shell  with  them.  Who  knows  how  many  shells  Ella  has  ? 

Peter  may  take  five  pictures.  He  raay  take  one  more 
picture.     Who  knows  how  many  pictures  Peter  has  ? 

Annie  may  pick  out  five  red  stars  and  one  blue  star. 
How  many  stars  has  Annie  ? 

Find  five  things  of  one  color  and  one  of  another  color, 
and  tell  me  how  many  you  have. 

If  I  find  five  raisins  in  one  piece  of  cake,  and  one  in 
another,  how  many  do  I  find  in  all  ? 

If  I  give  you  a  five-cent  piece,  and  a  one-cent  piece, 
how  many  cents  do  I  give  you  ? 

If  you  write  a  word  on  your  slate  five  times,  and  then 
write  it  once  more,  how  many  times  do  you  write  it? 

Tell  me  a  story  about  five  articles  and  one  article ;  an- 
other; another. 

One  and  Five. 

Alice  may  show  me  one  pail.  John  may  show  me  five 
more  pails.     How  many  pails  do  both  show  me  ? 

Jamie  may  give  one  blue  stick  to  Jennie,  and  five  red  sticks 
to  Nellie.     Who  will  tell  me  how  many  sticks  both  have? 

Make  one  mark  on  the  board  with  this  yellow  crayon, 
and  five  marks  with  this  blue  crayon.  How  many  marks 
have  you  made  ? 

Make  one  large  dot  on  the  board  with  this  green  crayon, 
and  five  dots  with  the  red  crayon.  How  many  dots  have 
you  made  ? 

Show  me  one  spool ;  put  five  with  it ;  how  many  now  ? 

Show  me  one  top  ;  put  five  with  it ;  how  many  now  ? 


THE   NUMBER  SIX.  59 

Show  me  one  paper  shovel ;  put  fiwe  paper  shovels  with 
it ;  how  many  paper  shovels  are  there  now  ? 

Show  me  one  paper  hat ;  put  five  paper  hats  with  it ; 
how  many  paper  hats  are  there  now  ? 

If  there  is  one  girl  standing  to  read,  and  five  more  stand 
with  her,  how  many  are  standing  ? 

If  Annie  uses  one  sheet  of  paper  in  the  morning,  and  five 
in  the  afternoon,  to  write  her  story,  how  many  sheets  of 
paper  does  she  use  ? 

If  you  put  one  j)late  on  the  table,  and  mamma  puts  on 
five  more,  how  many  plates  are  put  on  the  table  ? 

If  Nellie  has  five  little  girls  to  visit  her  on  her  birthday, 
how  many  little  girls  are  there  in  all  ? 

If  Johnnie  has  one  cent,  and  earns  fiwe  more,  how  many 
cents  does  he  earn  in  all  ? 

If  there  is  one  cruet  in  the  caster,  and  you  put  in  the 
other  fivCj  how  many  cruets  in  the  caster  ? 

Tell  me  a  story  about  one  and  five ;  another ;  another ; 
another. 

Exercise  for  Review. 

If  I  have  five  letters  to  write,  and  write  one  a  day,  how 
many  days  will  it  take  me  to  write  them  ? 

If  Annie  puts  her  two  hands  under  the  table,  and  Jamie 
puts  his  hands  under  the  table,  how  many  hands  will  there 
be  under  the  table? 

If  Ned  stands  squarely  on  two  feet,  and  Harry  stands 
squarely  on  two  feet,  how  many  feet  will  rest  nicely  on  the 
floor? 

If  there   are  three  in  your  family,  and  you  expect  two 
more  to  tea,  how  many  will  there  be  to  tea  ? 
'  How  many  cups  and  saucers  will  it  take  for  all  ?  how 
many  plates  ?  how  many  knives  and  forks  ? 

If  you  set  the  chairs,  how  many  chairs  will  you  place  ? 


60  FIRST  STEPS   IN   NUMBER. 

If  there  are  four  persons  in  your  family,  and  one  goes 
away  to  visit,  then  two  come  to  visit  you,  and  one  of  these 
goes  away,  hpw  many  will  there  be  in  the  family  ? 

If  you  have  two  errands  to  do  at  the  grocer's,  and  one 
at  the  jeweller's,  and  one  at  the  post  office,  how  many 
errands  have  you  to  do  in  all  ?  If  you  forget  three  of  your 
errands,  how  many  do  you  remember  ? 

If  you  have  four  errands  to  do,  and  forget  half  of  them, 
how  many  do  you  remember  ? 

If  you  have  four  miles  to  go,  and  go  two  miles,  what  part 
of  your  journey  have  you  made  ? 

Six  minus  One. 

Show  me  six  blocks.  We  will  call  them  ducks  in  a  pond. 
Mrs.  Bond  went  down  to  the  pond  and  caught  one ;  how 
many  were  left  ? 

Call  them  boats  sailing  by  ;  one  takes  in  sail ;  how  many 
go  sailing  on  ? 

We  will  call  them  frogs  ;  one  has  jumped  into  the  pond  ; 
how  many  are  left  ? 

Call  them  snails  creeping  into  their  shells ;  one  has  crept 
in ;  how  many  are  still  creeping  in  ? 

Call  them  mice  in  a  box  ;  one  has  jumped  out ;  how 
many  remain  in  the  box  ? 

If  you  have  six  cents,  and  buy  a  stick  of  candy  for  one 
cent,  how  many  cents  have  you  left  ? 

If  there  are  six  cakes  in  the  jar,  and  you  eat  one,  how 
many  cakes  remain  in  the  jar? 

If  Annie  has  six  stories  to  write,  and  writes  one,  how 
many  more  has  she  to  write  ? 

If  there  are  six  cows,  and  one  jumps  over  the  moon,  how 
many  are  left  ? 

If  you  have  six  dolls,  and  break  one,  how  many  are  left  ? 


THE   NUMBER   SIX.  61 

If  you  have  six  torpedoes,  and  snap  one,  how  many  have 
you  left? 

If  you  have  written  six  words,  and  one  is  wrong,  so  it 
has  to  be  rubbed  out,  how  many  will  remain  ? 

If  there  are  six  roses  on  a  bush,  and  one  drops  off,  how 
many  are  left? 

Six  minus  Five. 

Here  are  six  scholars  in  a  class ;  five  are  girls ;  how 
many  are  boys? 

There  are  six  weekdays  in  the  week ;  you  go  to  school 
five  days ;  how  many  days  do  you  have  to  play  at  home  ? 

There  were  six  monkeys  in  a  tree ;  five  were  small,  and 
the  rest  large ;  how  many  large  monkeys  in  the  tree? 

If  there  are  six  steps  to  go  up,  and  you  go  up  five,  how 
many  more  are  there  to  go  up  ? 

If  Mary's  doll  has  six  dresses,  and  she  puts  away  five, 
how  many  does  she  leave  out? 

If  there  are  six  stars  around  the  moon,  and  a  cloud 
covers  five,  how  many  can  you  see  ? 

If  you  have  six  pins,  and  I  take  five,  how  many  do  you 
have? 

Six  apples  are  in  a  dish ;  five  are  good  ;  how  many  bad  ? 

Exercise  for  Review. 

You  may  tell  me  a  story  about  six  minus  one ;  five  minus 
one  ;  four  minus  one  ;  three  minus  one  ;  two  minus  one. 

You  may  tell  me  a  story  about  five  minus  two  ;  four 
minus  two  ;  three  minus  two  ;  two  minus  two. 

Give  me  an  example  for  what  I  show  you.  (Teacher 
shows  different  combinations  and  separations  of  numbers 
with  the  blocks,  and  pupil  makes  an  example,  illustrating 
what  he  sees.) 


62  FIRST  STEPS   IN   NUMBER. 

If  you  drop  six  kernels  of  corn  into  each  hill,  and  a  worm 
eats  one,  a  crow  eats  two,  and  one  dies,  how  many  are  left 
to  grow  ? 

Show  me  six  blocks ;  six  fingers ;  six  marks  on  the 
board  ;  six  paper  baskets  ;  six  birds. 

Tell  me  what  number  I  show  you  ;  now  ;  now. 

If  you  have  six  presents  Christmas,  and  give  one  to  your 
brother,  how  many  presents  have  you  then  ? 

If  mamma  then  makes  you  another  present,  how  many 
will  you  have  ? 

I  have  one  bird's-nest  in  my  room,  and  my  sister  has 
five  ;  how  many  have  we  together  ? 

One  swallow  built  his  nest  on  a  beam  in  our  barn,  and 
five  more  built  nests  under  the  eaves ;  how  many  swallows' 
nests  were  there  in  all  ? 

Baby  is  one  year  old  to-day;  how  old  will  he  be  in  five 
more  years  ? 

Nellie  bought  six  pencils  this  morning,  but  has  already 
broken  one  ;  how  many  whole  ones  has  she  ^ 

When  she  has  broken  two  more,  how  many  will  she  have? 

Four  and  Two. 

Show  me  six  blocks. 

Show  me  four  of  them  ;  show  me  two  more.  How  many 
blocks  are  four  blocks  and  two  blocks?  How  many  sleds  are 
four  sleds  and  two  sleds?  How  many  knives  are  four 
knives  and  two  knives?  How  many  flies  are  four  flies  and 
two  flies?  How  many  bees  are  four  bees  and  two  bees? 
How  many  ants  are  four  ants  and  two  ants  ? 

Tell  me  a  story  about  four  handkerchiefs  and  two  hand- 
kerchiefs ;  four  sparrows  and  two  sparrows ;  four  cows  and 
two  horses  ;  four  hammers  and  two  gimlets ;  four  rakes 
and  two  pitchforks  ;  four  chairs  and  two  tables ;  four  books 
and  two  pencils ;  four  maps  and  two  pictures. 


THE  NUMBER  SIX.  63 

Two  and  Four. 

Show  me  two  blocks ;  now  show  me  four  more ;  how 
many  blocks  in  all  ? 

Show  me  two  beads ;  show  me  four  more ;  how  many 
beads  in  all  ? 

If  there  are  two  wheels  on  one  carriage,  and  four  on  an- 
other, how  many  wheels  altogether  ? 

If  a  whistle  costs  two  cents,  and  a  top  four  cents,  how 
many  cents  do  both  cost  ? 

If  your  boots  cost  two  dollars,  and  mine  cost  four  dollars, 
how  many  dollars  do  both  cost? 

If  a  pencil  cost  two  cents,  and  some  paper  four  cents, 
how  many  cents  do  both  cost? 

It  is  two  miles  to  church,  and  four  miles  more  to  the 
depot ;  how  many  miles  is  it  to  the  depot  ? 

Exercise  for  Revie^v. 

If  you  have  six  cents,  and  spend  five,  how  many  cents 
have  you  ? 

If  you  must  write  your  words  six  times,  and  have  writ- 
ten them  five  times,  how  many  more  times  must  you  write 
them? 

If  there  are  six  ponds  in  the  park,  and  all  but  one  have 
lilies  in  them,  how  many  have  lilies  in  them  ? 

If  there  are  six  boys  coasting  on  the  hill,  and  all  but  one 
come  in,  how  many  come  in  ? 

If  four  boys  are  skating  on  the  pond,  and  two  more  join 
them,  how  many  are  then  skating  on  the  pond  ? 

You  can  sing  four  songs ;  if  you  learn  to  sing  two  more, 
how  many  can  you  then  sing  ? 

It  is  two  miles  to  church  ;  if  I  walk  to  church  and  back, 
how  many  miles  do  I  walk? 


64  FIRST  STEPS   IN   NUMBER. 

How  many  miles  is  it  half  way  to  church  ? 

If  I  walk  half  way  to  church,  then  ride  the  rest  of  the 
way,  but  walk  home,  how  many  miles  shall  I  walk  ? 

Show  me  one-half  of  four  blocks  ;  one-half  of  two  blocks  ; 
one-half  of  six  blocks. 

Your  slate  has  four  sides ;  if  the  frame  is  gone  from  half 
the  sides,  from  how  many  sides  is  it  gone  ? 

There  are  four  boys  in  the  J)  class ;  one-half  of  the  class 
was  absent  yesterday  ;  how  many  were  absent  ? 

I  can  pick  a  pint  of  berries  in  half  an  hour ;  how  many 
pints  can  I  pick  in  an  hour  ? 

One  mile  is  half  the  distance  I  walk  every  pleasant  day ; 
how  many  miles  do  I  walk  ? 

What  time  does  the  minute-hand  take  to  go  round  the 
face  of  the  clock  ?  What  time  does  the  hour-hand  take  to 
go  half-way  round  the  face  of  the  clock?  What  part  of  the 
face  of  the  clock  does  the  minute-hand  go  round  in  half  an 
hour  ?  What  part  of  the  face  of  the  clock  does  the  hour- 
hand  go  round  in  six  hours  ? 

There  are  two  rounds  on  one  side  of  a  chair,  two  on  an- 
other side,  one  in  front,  and  one  behind  ;  how  many  rounds 
on  the  chair  ? 

How  many  sides  has  this  room  ?  If  you  count  the  ceil- 
ing and  the  floor,  how  many  sides  has  it  ? 

Six  minus  Two. 

Show  me  six  fingers;  shut  two  fingers;  how  many  fingers 
are  open? 

Show  me  six  blocks  minus  two  blocks.  Tell  me  a  story 
about  six  blocks  minus  two  blocks ;  six  horses  minus  two 
horses  ;  six  beans  minus  two  beans  ;  six  cushions  minus  two 
cushions ;  six  dolls  minus  two  dolls ;  six  books  minus  two 
books  ;  six  lamps  minus  two  lamps ;  six  candles  minus  two 


THE   NUMBER  SIX.  65 

candles  ;  six  postal  cards  minus  two  postal  cards  ;  six  enve- 
lopes minus  two  envelopes ;  six  sheets  of  paper  minus  two 
sheets  of  paper ;  six  pints  of  molasses  minus  two  pints  of 
molasses ;  six  plates  minus  two  plates ;  six  sticks  minus  two 
sticks ;  six  umbrellas  minus  two  umbrellas ;  six  Christmas 
trees  minus  two  Christmas  trees ;  six  presents  minus  two 
presents  ;  six  pop-guns  minus  two  pop-guns. 

Six  minus  Four. 

Make  six  straight  lines  on  the  board ;  ^cross  out  four  of 
them ;  how  many  are  not  crossed  out  ? 

Show  me  six  o's  on  the  board  ;  cross  out  four  ;  how  many 
are  not  crossed  out  ? 

Show  me  six  crosses  on  the  board ;  cross  out  four  of 
them  ;  how  many  are  not  crossed  out  ? 

Show  me  six  slanting  lines  ;  cross  out  four ;  how  many 
are  uncrossed? 

Show  me  six  dots ;  draw  a  line  through  four  of  them ; 
how  many  have  no  line  drawn  through  them  ? 

Show  me  six  blocks,  and  tell  me  how  many  blocks  six 
blocks  minus  four  blocks  are. 

Tell  me  another  story  about  six  minus  four ;  another ; 
another. 

Exercise  for  Review. 

How  many  eyes  and  ears  have  you  ?  how  many  hands 
and  feet? 

If  you  must  pick  up  your  mittens  and  your  boots,  how 
many  things  must  you  pick  up  ?  If  then  you  see  your  hat 
and  coat  lying  on  the  chair,  and  pick  them  up,  how  many 
things  do  these  make  that  you  had  to  pick  up? 

If  there  is  a  bed,  and  two  chairs,  and  a  table,  and  chest 
of  drawers  in  your  room,  how  many  articles  of  furniture  in 


66  FIRST  STEPS   IN   NUMBER. 

your  room?  If  then  you  have  a  bookcase  put  up,  how 
many  pieces  of  furniture  will  there  be  ? 

If  there  are  four  books  on  your  bookcase,  and  two  on  the 
table,  how  many  books  are  there  ? 

If  Johnny  pays  two  cents  for  a  pencil,  and  three  cents 
for  a  sponge,  how  many  cents  does  he  pay  ? 

If  I  buy  two  Christmas  cards  at  two  cents  apiece,  and 
another  for  two  cents,  how  many  cents  will  all  three  cost  ? 

There  are  six  parts  to  Harry's  puzzle  ;  he  cannot  find  two 
parts  ;  how  many  parts  can  he  find  ? 

How  many  legs  have  you  and  your  dog  together  ? 

How  many  feet  have  you  and  your  cat  together  ? 

How  many  feet  and  ears  has  your  dog  ? 

How  many  blinds  do  you  see  on  two  windows? 

How  many  mittens  make  two  pairs  of  mittens  and  a  half 
a  pair  ? 

How  many  boots  make  two  and  a  half  pairs  of  boots  ? 

If  it  takes  half  a  minute  to  write  half  of  your  words,  how 
long  will  it  take  to  write  the  whole  ? 

If  I  receive  two  express  packages,  send  one  back,  then 
receive  two  more,  how  many  do  I  keep  ? 

If  I  can  paint  one  placque  in  two  hours,  how  long  will 
it  take  me  to  paint  two  such  placques  ? 

Two  cards  and  four  cards  are  how  many  cards  ? 

Three  books  and  two  books  are  how  many  books  ? 

'  §  17.    The  Inch. 

(Provide  some  stiff  squares,  an  inch  on  each  side.) 

You  may  each  take  one  of  these  squares. 

Show  me  one  side  of  your  square.  Who  knows  how  long 
it  is? 

Ned  says  it  is  an  inch  long.     It  is  an  inch  long. 

Draw  on  the  board  a  line  an  inch  long ;  measure  it  by  a 
side  of  your  square  so  as  to  be  sure  it  is  an  inch  long. 


THE   NUMBER  SIX.  67 

Draw  another  line  an  inch  long. 

Draw  an  up-and-down  line  an  inch  long. 

Draw  a  right-and-left  line  an  inch  long. 

Draw  a  slanting  line  an  inch  long. 

Here  are  some  strips  of  paper  marked  off  into  squares. 
Find  how  long  it  is  between  any  two  marks.     (An  inch.) 

See  if  it  is  an  inch  between  the  joints  on  your  fingers  ; 
between  the  joints  on  your  hand. 

Measure  this  side  of  this  block.     Is  it  an  inch  long  ? 

This  side  of  the  block.     Is  it  an  inch  ? 

Measure  this  side  of  this  card. 

Measure  this  side  of  this  envelope. 

Measure  this  side  of  this  postage-stamp  ;  this  side  of  this 
little  book  ;  an  edge  of  this  rubber  ;  of  this  little  box. 

Measure  this  knife-handle ;  the  blade  ;  this  pencil ;  a 
side  of  this  square  I  draw  on  the  board. 

You  may  draw  a  line  two  inches  long;  three  inches  long; 
four  inches  long  ;  five  inches  long. 

You  may  guess  how  long  this  line  is  that  I  draw ;  this 
line  ;  this  line. 

If  it  takes  two  inches  of  edging  to  go  round  one  sleeve 
of  dolly's  dress,  how  many  inches  will  it  take  to  trim  the 
two  sleeves?  If  it  takes  two  more  inches  to  trim  the  neck, 
how  many  inches  will  it  take  in  all  ? 

Six  divided  by  Two. 

You  may  divide  your  six  blocks  as  I  divide  mine. 


How  many  in  each  group?  How  many  groups  of  two 
each? 

Take  six  paper  cents,  and  see  if  you  can  find  three  twos 
in  six.     Take  six  sticks;  take  six  circles;  take  six  cards. 


68  FIRST  STEPS   m   NUMBER. 

If  you  had  six  apples,  and  should  put  two  on  a  plate,  how 
many  plates  would  you  need  ? 

If  you  had  six  cents,  how  many  two-cent  stamps  could 
you  buy  ?  How  many  two-cent  pencils  ?  How^  many  tw^o- 
cent  books  ?     How  many  two-cent  spools  of  thread  ? 

If  I  have  six  boots,  how  many  pairs  have  I  ? 

If  there  are  six  horses  on  a  stage-coach,  how  many  spans 
of  horses  are  there  ? 

If  a  man  has  six  oxen,  how  many  yokes  of  oxen  has  he  ? 

It  takes  two  horses  for  every  hack ;  how  many  hacks  will 
six  horses  supply  ? 

If  you  owe  me  six  cents,  and  pay  me  in  two-cent  pieces, 
how  many  pieces  will  you  give  me  ? 

If  I  have  six  half  sticks  of  candy,  how  many  whole  sticks 
of  candy  have  I  ? 

I  have  six  screws  which  I  am  going  to  put  into  picture- 
frames.  I  shall  put  two  in  each  frame.  How  many  frames 
are  there  ? 

It  takes  two  tassels  for  every  curtain.  If  I  have  six  tas- 
sels, how  many  curtains  can  I  furnish  with  tassels  ? 

Three  Twos. 

Show  me  two  blocks  together ;  two  more  together ;  two 
more  together.  How  many  twos?  How  many  blocks  in 
all? 

Show  me  two  buttons ;  another  two  buttons  ;  another  two 
buttons.     How  many  buttons  in  all  ? 

Show  me  three  boxes  ;  ]3ut  two  cents  in  each  box.  How 
many  cents  in  all  ? 

Show  me  three  tin  plates ;  put  two  pieces  of  paper  in 
each  plate.     How  many  pieces  of  paper  in  all  ? 

If  you  have  three  pockets,  and  two  apples  in  each  pocket, 
how  many  apples  will  you  have  ? 


THE   NUMBER  SIX.  69 

If  you  buy  three  pencils,  and  pay  two  cents  for  each 
pencil,  how  many  cents  must  you  pay? 

If  there  are  three  little  boys  looking  straight  at  me,  how 
many  eyes  will  be  looking  at  me  ? 

If  three  little  boys  have  their  hands  under  the  table,  how 
many  hands  are  under  the  table  ? 

How  many  mittens  will  it  take  for  three  girls  ? 

How  many  wristers  for  James,  John,  and  Willie  ? 

How  many  skates  for  three  boys  ? 

If  Mary  writes  two  stories  each  day,  for  three  days,  how 
many  stories  will  she  write  ? 

If  Harry  finds  three  hen's  nests,  with  two  fresh  eggs  in 
each  nest,  how  many  eggs  does  he  find  ? 

Each  sheet  of  paper  has  two  leaves,  how  many  leaves 
have  three  sheets  ? 

If  each  ink-stand  has  two  wells  for  ink,  how  many  wells 
will  three  such  ink-stands  have  ? 

If  a  bottle  of  ink  will  fill  two  of  the  ink-stand  wells,  how 
many  wells  will  three  bottles  fill  ? 

Three  and  Three. 

Each  choose  three  things  of  the  same  kind.  Choose 
three  more  like  them.     Who  will  tell  me  how  many  he  has  ? 

Who  has  a  story  for  what  he  has  shown  me  ? 

Find  three  squares  on  this  chart.  Find  three  more 
squares.    How  many  squares  have  you  found  all  together  ? 

Find  three  stars  and  three  stars ;  three  rings  and  three  rings. 

Three  spools  and  three  spools  are  how  many  spools  ? 

Three  marks  on  the  board  and  three  marks  on  the  board 
are  how  many  marks  ? 

Three  apples  and  three  apples  are  how  many  apples  ? 

Three  chairs  and  three  chairs  are  how  many  chairs  ? 

Three  marbles  and  three  marbles  are  how  many  marbles? 

Tell  me  a  story  about  three  and  three ;  another ;  another. 


70  FIRST  STEPS   IN   NUMBER. 

Exercise  for  Review. 

Show  me  six  blocks ;  six  buttons ;  six  shells ;  six  fingers ; 
six  inch-measures. 

Show  me  five  fingers;  five  bits  of  crayon;  five  pieces  of 
paper. 

How  many  must  you  take  away  from  six  blocks  to  have 
four  remain  ?  to  have  three  remain  ?  to  have  two  remain  ? 

Tell  me  a  story  about  six  minus  four;  six  minus  two;  six 
minus  five. 

Name  six  books  you  have  seen. 

Name  six  towns  of  which  you  have  heard. 

Name  six  games  that  you  can  play. 

Give  six  stories  that  you  can  write. 

Give  six  words  that  you  can  spell. 

Name  six  animals  that  you  know. 

How  many  mittens  in  three  pairs  of  mittens  ? 

How  many  horses  in  three  spans  of  horses  ? 

How  many  oxen  in  three  yokes  of  oxen  ? 

Which  will  buy  more  peanuts,  six  cents  or  three  two- 
cent  pieces? 

Which  cost  the  more,  six  one-cent  pencils  or  three  two- 
cent  pencils? 

I  can  see  three  flies  and  two  bees  ;  how  many  insects  can 
I  see? 

If  a  spider  catches  two  flies  in  his  web  to-day  and  four 
to-morrow,  how  many  flies  will  he  catch  altogether  ? 

You  may  divide  this  apple  into  two  equal  parts.  What 
part' of  the  whole  number  is  each  part? 

Divide  this  string  into  two  equal  parts.  What  part^pf 
the  whole  string  is  each  part  ?  How  many  halves  in  the 
whole  string? 

This  stick  is  two  inches  long.  How  long  is  half  the 
stick? 


THE   NUMBER  SIX.  71 

Six  minus  Three. 

How  many  blocks  have  I  ?     (Six.) 

How  many  will  you  take,  then  ? 

I  will  give  you  three  of  my  blocks ;  how  many  have  I 
left? 

Nellie,  you  may  give  Harry  three  of  your  blocks ;  how 
many  have  you  left  ? 

Jennie,  you  may  give  me  three  of  your  six  blocks  ;  how 
many  have  you  left? 

Tell  me  a  story  about  six  chickens  minus  three  chickens; 
six  sheets  of  paper  minus  three  sheets  of  paper ;  six  books 
minus  three  books ;  six  plates  minus  three  plates  ;  six  spoons 
minus  three  spoons ;  six  bonnets  minus  three  bonnets ;  six 
dollars  minus  three  dollars;  six  umbrellas  minus  three  um- 
brellas ;  six  baskets  minus  three  baskets  ;  six  marbles  minus 
three  marbles  ;  six  watches  minus  three  watches. 


Six  divided  by  Three. 

Show  me  six  blocks.  Divide  your  blocks  as  I  divide 
mine. 

0     0     0  0     0     0 

How  many  here  ?  here  ?     How  many  threes  ? 

Take  six  blocks  of  another  kind.  See  if  you  can  find  how 
many  three-blocks  in  six  blocks.      How  many  do  you  find  ? 

Take  six  crayons  and  put  three  on  a  board.  How  many 
boards  can  you  put  them  on  ? 

Here  are  six  cows.  Put  three  in  a  pen.  How  many 
pens  does  it  take  ? 

If  I  have  six  cents,  how  many  three-cent  postage-stamps 
can  I  buy?  how  many  three-cent  books?  how  many  three- 
cent  pencils?  how  many  three-cent  rubbers? 


72  FIRST   STEPS   IN   NUMBER. 

If  I  have  six  books,  and  put  three  on  a  shelf,  how  many 
shelves  will  it  take  ? 

If  there  aTe  six  sticks  of  wood  in  the  box,  and  you  put 
three  in  the  stove  at  once,  how  many  times  can  you  put 
three  in  the  stove  before  they  are  gone  ? 

If  there  are  six  little  girls,  and  three  walk  in  each  row, 
how  many  rows  of  girls  ? 

Exercise  for  Review. 

If  two  boats  start  at  the  same  place,  and  one  rows  up  the 
river  three  miles,  and  the  other  rows  down  the  river  three 
miles,  how  far  apart  are  the  two  boats? 

If  a  spider  in  spinning  his  web  spins  a  thread  three 
inches  in  one  direction  and  three  inches  in  the  opposite 
direction,  how  far  across  is  the  web  ? 

If  two  men  are  six  miles  apart,  and  walk  towards  each 
other  three  miles,  how  far  apart  are  they  then? 

Here  are  six  pencils ;  two  of  them  are  too  short  to  use, 
and  three  others  are  too  blunt  to  write  well.  How  many 
are  in  a  good  condition  ? 

I  have  two  hens,  a  duck,  and  a  goose  ;  how  many  fowls 
have  I? 

Ned  has  three  tame  rats,  two  rabbits,  and  a  young  fox ; 
how  many  pets  has  he  ? 

If  there  are  six  hoods  on  the  chair,  and  Annie  hangs  up 
three  of  them,  how  many  are  left  on  the  chair  ? 

If  you  must  bring  in  four  baskets  of  wood,  and  have 
already  brought  in  two,  how  many  more  must  you  bring  in? 

If  you  must  pick  up  your  doll,  put  away  your  blocks, 
sweep  the  room,  and  set  the  chairs  in  order,  how  many 
things  must  you  do  ? 

In  one  nest  there  are  four  eggs,  and  in  another  two 
eggs.  If  I  leave  the  nest-egg  only  in  each  nest,  how  many 
eggs  shall  I  take  away  ? 


THE   NUMBER  SIX.  73 

Two  Threes. 

Show  me  three  blocks. 

Show  me  another  three  blocks. 

How  many  threes?  Your  two  three-blocks  are  how 
many  blocks  ? 

Take  three  spools  and  another  three  spools.  How  many 
threes  ?     How  many  spools  in  all  ? 

Show  me  three  blocks  in  each  of  your  two  hands.  How 
many  threes  do  you  show  me  ?     How  many  blocks  ? 

I  have  three  buttons  on  each  pocket.  How  many  but- 
tons have  I  on  my  two  pockets  ? 

There  are  three  dots  on  each  of  these  two  cards.  How 
many  dots  in  all  ? 

If  a  sponge  costs  three  cents,  how  many  cents  will  two 
sponges  cost  ? 

If  Ellen  writes  three  i's  on  each  line,  how. many  will  she 
write  on  two  lines  ? 

If  there  are  three  rings  on  each  finger,  how  many  rings 
on  two  fingers  ? 

Exercise  for  Review. 

Point  in  four  directions  ;  point  in  two  more  directions. 
In  how  many  directions  have  you  pointed  ? 

Put  a  block  on  each  corner  of  the  table.  How  many 
blocks  does  it  take  ? 

Take  two  shells  in  each  hand.  How  many  shells  have  you? 

Every  chair  has  a  seat,  four  legs,  and  a  back.  How 
many  parts  has  every  chair  ? 

If  Jamie  has  six  marbles,  and  loses  two,  then  buys  two 
more,  how  many  marbles  has  he? 

If  Nellie  writes  four  words,  erases  three  words,  then 
writes  three  more  words,  how  many  words  has  she  on  her 
slate  ? 


74  FIRST   STEPS    IN   NUMBER. 

If  Mabel  has  some  pennies,  and  spends  four,  tlien  earns 
four,  how  many  more  pennies  has  she  than  at  first? 

If  I  have  five  dollars,  and  spend  three,  then  receive  four, 
how  many  more  have  I  than  at  first  ? 

You  may  arrange  six  dots  on  the  board  in  all  the  ways 
you  can. 

You  may  arrange  six  lines  on  the  board  in  all  the  ways 
you  can. 

Eead  what  I  show  you  ;  read  again  ;  read  again. 

Make  up  a  story  from  what  I  show  you  with  the  blocks. 

Make  up  a  story  from  what  I  show  you  on  the  board. 

You  may  tell  me  any  story  you  know  about  six,  and  I 
will  illustrate  it  on  the  board.     Tell  me  another  ;  another. 

*  I  will  give  you  an  example,  and  you  may  illustrate  on 
the  board  what  I  tell  you. 

Ned  has  illustrated  five  examples,  and  Mamie  three. 
How  many  more  has  Ned  illustrated  than  Mamie  ? 

Six  minus  Six. 

If  I  have  six  cents,  and  buy  a  six-cent  loaf  of  bread,  how 
many  cents  have  I  left  ?    Show  me  with  your  blocks. 

If  there  are  six  rolls  on  the  plate,  and  if  six  of  us  take 
each  a  roll,  how  many  rolls  are  left? 

I  will  give  you  these  six  cents.  You  may  buy  me  six 
one-cent  stamps  ;  how  many  cents  have  you  left  ? 

If  a  lady  has  six  peppermints,  and  she  gives  to  each  of 
six  little  girls  one  peppermint,  how  many  will  she  have  left  ? 

Six  oranges  minus  six  oranges  are  how  many  oranges  ? 

Six  spiders  minus  six  spiders  are  how  many  spiders  ? 

Six  elephants  minus  six  elephants  are  how  many  ele- 
phants ? 

*  If  the  teacher  is  judicious  in  her  examples,  and  encouraging  in  regard 
to  the  illustrations,  this  is  one  of  the  most  profitable  exercises  in  Arithmetic. 


THE   NUMBER  SIX.  75 

Exercise  for  Review. 

If  I  have  no  money,  and  no  one  gives  me  any  money, 
how  much  money  shall  I  have  ? 

If  James  has  no  words  on  his  slate,  and  writes  no 
words  on  his  slate,  how  many  words  will  there  be  on  his 
slate  ? 

If  there  are  no  blocks  on  the  table,  how  many  blocks  can 
you  take  from  the  table  ? 

If  there  are  no  apples  in  the  dish,  how  many  apples  can 
you  take  from  the  dish  ? 

If  there  are  no  hats  or  coats  lying  around,  how  many 
hats  and  coats  will  there  be  to  pick  up  ? 

If  there  are  no  oranges  in  town,  how  many  oranges  can  I 
buy  in  town? 

If  there  are  no  mistakes  on  your  slate,  how  many  mis- 
takes will  you  have  to  correct  ? 

If  no  May-flowers  have  blossomed,  how  many  May-flowers 
can  you  find  ? 

If  there  are  no  books  on  the  desk,  and  I  put  four  books 
on  the  desk,  how  many  books  will  there  be  on  the  desk  ? 

If  there  is  no  milk  in  the  pan,  and  I  put  three  pints  of 
milk  in  the  pan,  how  much  milk  will  there  be  in  the 
pan? 

If  three  little  girls  have  each  two  pencils,  how  many  pen- 
cils have  they  together  ? 

If  each  girl  has  one  pencil,  how  many  pencils  have  they  ? 

If  each  girl  has  no  pencil,  how  many  pencils  have  they  ? 

If  each  of  four  boys  had  no  cents,  how  many  cents  would 
all  have  ? 

If  one  velocipede  has  three  wheels,  how  many  wheels 
have  two  velocipedes  ? 

How  many  chairs  in  two  chambers,  if  there  are  three  in 
each  chamber  ? 


76  FIRST  STEPS   IN   NUMBER. 

Six  divided  by  One. 

Take  six  buttons ;  put  each  on  a  plate  by  itself.  How 
many  plates  does  it  take  ? 

Here  are  six  cups;  put  each  in  a  saucer  by  itself.  How 
many  saucers  does  it  take  ? 

Here  are  six  spoons ;  put  each  in  a  saucer.  How  many 
saucers  are  required  for  the  six  spoons,  with  each  one  in  a 
saucer  by  itself? 

Here  are  six  cents ;  give  one  cent  to  each  little  girl  until 
they  are  all  given  away.  To  how  many  little  girls  can  you 
give  them  ? 

I  have  six  curtains.  I  shall  put  one  at  a  window.  How 
many  windows  will  they  supply  ? 

There  are  six  horses  in  a  stable ;  each  is  in  a  stall  by  it- 
self.    How  many  stalls  do  they  take  ? 

I  have  written  six  stories.  If  now  I  draw  a  picture  to 
illustrate  each  story,  how  many  pictures  must  I  draw  ? 

Exercise  for  Review. 

Draw  a  line  on  the  board  one  inch  long. 
Draw  another  line,  two  inches  in  length. 
What  part  of  the  last  line  is  the  first  ? 
Draw  a  line  twice  as  long  as  the  last  line. 
What  part  of  the  last  line  is  the  two-inch  line  ? 
Draw  a  line  three  inches  long. 
Draw  another  line  twice  as  long. 
What  part  of  the  last  line  is  the  three-inch  line  ? 
Show  me  a  line  four  inches  long. 
Show  me  a  line  half  as  long  as  the  four-inch  line. 
Show  me  the  line  that  is  six  inches  long. 
Point  to  a  line  half  as  long. 

The  one-inch  line  is  half  as  long  as  what  other  line  on 
the  board? 

The  three-inch  line  is  equal  to  one-half  of  what  line  ? 


THE   NUMBER  SIX.  77 

Six  Ones. 

Take  six  blocks.  Put  them  as  I  put  mine.  (Teacher 
separates  hers  into  ones.) 

How  many  ones  have  you  ? 

How  many  blocks  altogether  ? 

Show  me  six  shells,  with  a  pebble  in  each  shell ;  how 
many  pebbles  do  you  show  me  ? 

Show  me  six  cards,  with  a  dot  on  each  card  ;  how  many 
dots? 

If  there  are  six  wagons  front  of  the  market,  and  a  driver 
in  each  wagon,  how  many  drivers  are  there  ? 

If  Amy  learns  a  word  each  day  for  six  days,  -how  many 
words  will  she  have  learned  ? 

If  six  of  us  have  each  an  orange,  how  many  oranges  have 
we  together  ? 

If  six  boys  have  each  a  sled,  and  put  them  together  in 
line,  how  many  sleds  will  be  in  line  ? 

If  six  little  girls  agree  each  to  make  an  apron  for  the 
fair,  how  many  aprons  will  they  make  for  the  fair  ? 

If  six  little  girls  agree  each  to  dress  a  doll,  how  many 
dolls  will  they  dress  ? 

If  I  write  my  name  on  each  of  six  visiting  cards,  how 
many  times  must  I  write  my  name  ? 

Who  will  tell  me  a  story  about  six  ones  ? 

Six  divided  by  Six. 

I  have  six  apples.  I  wish  to  give  six  apples  to  as  many 
little  boys  as  I  can.  Who  will  tell  me  to  how  many  little 
boys  I  can  give  them,  giving  six  apples  to  each? 

If  you  have  six  cents,  how  many  tops  at  six  cents  each 
can  you  buy  ?  How  many  cards  at  six  cents  each  ?  How 
many  toy  balloons  at  six  cents  each  ? 

A  car  ticket  costs  six  cents ;  how  many  car  tickets  can 
you  buy  if  you  have  only  six  cents  ? 


78  FIRST  STEPS   IN   NUMBER. 


Exercise  for  Review. 


You  may  divide  this  square  into  two  equal  parts ;  this 
circle ;  this  triangle  ;  this  string  ;  this  splint ;  this  line. 

Draw  a  line  dividing  this  blackboard  into  two  equaJ 
parts. 

Divide  four  blocks  into  two  equal  parts ;  into  four  equal 
parts. 

Divide  five  blocks  into  five  equal  parts. 

Divide  three  blocks  into  three  equal  parts. 

Divide  six  blocks  into  six  equal  parts ;  into  three  equal 
parts  ;  into  two  equal  parts. 

If  car  tickets  are  three  cents  apiece,  how  many  can 
you  buy  for  six  cents? 

How  many  postage-stamps  at  three  cents  each  can  you 
buy  for  six  cents  ? 

How  many  days  will  it  take  for  you  to  earn  six  cents,  if 
you  earn  three  cents  a  day? 

If  Mary  hems  three  handkerchiefs  in  a  week,  how  many 
weeks  will  it  take  her  to  hem  six  handkerchiefs  ? 

If  she  hems  only  two  a  week  how  many  weeks  will  it 
take  her  to  hem  six  ? 

If  Ellen  writes  two  words  a  minute,  how  many  minutes 
will  it  take  her  to  write  six  words  ? 

A  pint  of  milk  costs  two  cents,  how  many  pints  will  six 
cents  buy  ? 

It  requires  two  boys  to  steer  a  sled ;  how  many  sleds 
can  six  boys  manage  ? 

If  it  required  only  one  boy  to  steer  each  sled,  how  many 
could  six  boys  manage  ? 

How  many  one-cent  stamps  will  six  cents  buy  ? 

How  many  one-cent  rolls  will  six  cents  buy? 

If  Nellie  learns  one  stanza  a  day,  how  many  days  will  it 
take  her  to  learn  six  stanzas  ? 


THE  NUMBER  SIX.  79 

If  I  have  six  cups  to  paint,  and  I  paint  one  a  day,  how 
many  days  will  it  take  me  to  paint  the  six  cups  ? 

How  many  six-cent  cards  can  I  buy  for  six  cents  ? 

How  many  three-cent  cards  ? 

How  many  two-cent  cards  ? 

How  many  one-cent  cards  ? 

How  many  five-cent  cards?  and  how  many  cents  will 
remain  ? 

How  many  four-cent  cards?  and  how  many  cents  will 
remain  ? 

Halves  of  Six. 

Show  me  six  splints.  Give  me  half  of  them.  How 
many  do  you  give  me? 

I  have  six  cents.  If  I  spend  half  of  what  I  have,  how 
many  cents  do  I  spend?  How  many  cents  have  I  left? 
What  part  of  six  cents  are  three  cents  ? 

Mary  has  six  sheets  of  paper ;  Annie  has  only  half  as 
many  sheets  ;  how  many  sheets  of  paper  has  Annie  ? 

The  cook  uses  six  eggs  to  make  a  pudding,  and  half  as 
many  to  make  a  loaf  of  cake  ;  how  many  eggs  does  she  use 
for  cake  ? 

Nellie  is  in  school  six  hours  a  day ;  her  little  sister  is  in 
school  only  half  as  many  hours ;  how  many  hours  is  her 
sister  in  school  ? 

I  work  six  days  in  the  week ;  my  sister  works  half  as 
many  days ;  how  many  days  does  she  work  ? 

Exercise  for  Review. 

Show  me  one-half  of  six  blocks. 
How  many  blocks  are  one-half  of  six  blocks  ? 
How  many  apples  are  one-half  of  six  apples  ? 
How  many  oranges  are  one-half  of  six  oranges  ? 


80  FIRST   STEPS   IN   NUMBER. 

I  have  here  six  nuts.  Belle,  I  will  give  you  half  of  them 
if  you  can  tell  me  how  many  that  number  is. 

Johnny  started  with  six  eggs  from  the  store,  but  broke 
half  of  them  before  he  got  home.  How  many  did  he  break? 
How  many  had  he  left  ? 

Three  bonnets  are  what  part  of  six  bonnets? 

You  have  shown  me  one  half  of  six ;  show  me  two  halves 
of  six. 

How  many  blocks  in  two  halves  of  six  blocks  ? 

How  many  apples  in  two  halves  of  six  apples  ? 

How  many  cents  in  two  halves  of  six  cents? 

How  many  nuts  in  two  halves  of  six  nuts  ? 

How  many  balls  in  one  half  of  six  balls  ?  in  two  halves 
of  six  balls  ? 

If  I  divide  six  cards  equally  between  two  girls,  how  many 
shall  I  give  to  each  girl  ?  What  part  of  the  whole  number 
will  each  have  ? 

§  18.   Comparison  of  Six  with  Numbers  Known. 

One  hen  had  six  chickens,  another  five  ;  how  many  more 
did  the  first  have  than  the  second  ? 

I  have  here  two  three-cent  stamps,  and  here  two  two- 
cent  stamps  and  a  one-cent  stamp.  Which  cost  the  more  ? 
How  much  more  ? 

Mary  has  six  cents  ;  I  have  four.  Which  has  the  more  ? 
How  many  more  has  Mary? 

Which  have  more  legs,  three  boys  or  a  chair  ?  two  boys 
or  a  chair?  two  boys  or  a  dog?  two  boys  or  a  hen? 

These  six  postal  cards  cost  a  cent  apiece ;  this  bunch  of 
envelopes  four  cents.  Which  cost  more  cents?  How  many 
more  cents? 

Here  are  three  two-cent  coins,  and  a  five-cent  coin ;  which 
is  worth  the  more  ?     How  much  more  ? 


THE   NUMBER  SIX.  81 

Mira  writes  six  stories  on  her  slate  while  Harry  is  writ- 
ing three.  Which  writes  the  more  stories  ?  How  many- 
more  does  Mira  write  ? 

In  one  half  a  window,  a  man  puts  six  panes  of  glass; 
he  has  four  panes  already  set ;  how  many  more  has  he  to 
set? 

I  have  written  six  letters,  and  I  find  I  have  only  four 
-envelopes  ;  how  many  more  do  I  need  ? 

In  a  half-dozen  there  are  six  things  ;  in  a  quarter  of  a 
dozen  three  things.  Which  had  you  rather  have,  a  half- 
dozen  sticks  of  candy,  or  a  quarter  of  a  dozen  ? 

One  basket  has  in  it  a  half-dozen  eggs,  and  another  a 
quarter  of  a  dozen.  How  many  more  has  the  one  than  the 
other? 

A  quire  of  one  kind  of  paper  costs  six  cents,  and  a  quire 
of  another  kind  four  cents ;  which  costs  the  more  ? 

Your  mother  pays  six  cents  a  pound  for  flour,  and  two 
cents  a  pound  for  meal.  How  much  more  does  the  flour 
cost  than  the  meal  ? 

Your  father  pays  six  dollars  for  his  boots,  and  two  dol- 
lars for  your  boots.  How  much  more  does  he  pay  for  his 
own  boots? 

Milk  is  six  cents  a  quart  in  the  winter,  and  four  cents  a 
quart  in  the  summer.  How  much  more  does  milk  cost  in 
the  winter  than  in  the  summer  ? 

Two  little  girls  were  hunting  for  pins.  One  found  six, 
and  the  other  found  one.  How  many  more  did  one  find 
than  the  other? 

Two  little  boys  were  bouncing  ball.  One  missed  six 
times,  and  the  other  once.  How  many  more  times  did  one 
miss  than  the  other  ? 

Show  me  six  blocks  in  a  row. 

Show  me  right  below  them  five  in  a  row. 

Right  below  the  five,  four  blocks  in  a  row. 


82  FIRST   STEPS    IN   NUMBER. 

Show  me  three  in  a  row ;  two  in  a  row. 

Show  me  one  beneath  them  all. 

Which  row  has  the  most  ? 

How  many  more  in  the  six-row  than  in  the  row  below  it  ? 

How  many  more  in  the  five-row  than  in  the  row  below  ? 

How  many  more  in  the  three-row  than  in  the  row  below? 

How  many  more  in  the  two-row  than  in  the  row  below? 

How  many  must  you  put  with  one  to  make  two  ? 

How  many  must  you  put  with  two  to  make  three  ? 

How  many  must  you  put  with  three  to  make  four  ? 

How  many  must  you  put  with  four  to  make  five? 

How  many  must  you  put  with  five  to  make  six  ? 

Show  me  six  dots  on  the  board  ;  put  below  them  one  dot. 

How  many  more  dots  in  six  dots  than  in  one  dot  ? 

Tell  me  a  story  about  this. 

Show  me  another  six  dots  on  the  board ;  put  below  them 
two  dots. 

How  many  more  in  six  than  in  two  ? 

Tell  me  a  story  about  this. 

Show  me  six  dots  with  three  dots  below  them. 

How  many  more  in  the  six  than  in  the  three  ? 

Tell  me  a  story  about  this. 

Show  me  six  dots  with  four  dots  below  them  ? 

How  many  more  in  the  six-row  than  in  the  four-row  ? 

Tell  me  a  story  about  this. 

Show  me  six  dots  with  five  dots  below  them. 

How  many  more  in  six  than  in  five  ? 

Tell  me  a  story  about  this. 

I  have  here  five  pencils.  I  own  six  pencils.  How  many 
more  have  I  than  I  show  you? 

I  have  five  cents  in  my  pocket.  I  need  six  cents  to  make 
change.     How  many  more  cents  must  I  have  ? 

Two  drawers  have  four  handles ;  three  have  six  handles. 
How  many  more  handles  have  three  drawers  than  two 
drawers? 


THE   NUMBER  SIX.  83 

Willie  has  learned  four  words,  George  six.  How  many 
more  words  has  George  learned  than  Willie  ? 

A  fly  has  six  legs.  How  many  more  legs  has  a  fly  than 
a  mouse  ? 

John  has  told  me  three  things  a  bird  can  do  ;  Mamie  has 
told  me  six.  How  many  more  things  did  Mamie  think  of 
than  John  ? 

Mary  has  six  dolls ;  Lena  half  as  many.  How  many 
more  has  Mary  than  Lena  ? 

A  pint  of  milk  costs  three  cents  ;  a  quart  six  cents.  How 
much  more  does  a  quart  cost  than  a  pint  ? 

Ned  had  but  two  cents,  and  wanted  a  six-cent  book. 
His  father  told  him  he  might  have  the  book  if  he  could  tell 
him  how  many  more  cents  he  needed  to  buy  it.  How 
many  more  cents  did  he  need  ? 

A  little  girl  has  filled  two  salt-cellars.  She  had  six  to 
fill  in  the  first  place.     How  many  more  has  she  to  fill  ? 

She  has  put  two  plates  on  the  table.  How  many  more 
must  she  put  on  to  have  six  on  the  table  ? 

Susie  is  two  years  old.  In  how  many  years  will  she  be 
six  years  old  ? 

Tottie  is  a  year  old.  In  how  many  years  will  sh^  be  six 
years  old? 

Nellie  is  five  years  old,  and  Jennie  one  year  old.  Which 
will  have  her  sixth  birthday  first  ? 

James  and  Susie  each  earn  a  cent  a  day.  James  has 
already  earned  four  cents,  and  Susie  three.  Which  must 
work  more  days  to  earn  six  cents?     How  many  more  days  ? 

Six  minus  one  are  how  many  ? 

Six  minus  two  are  how  many  ? 

Six  minus  three  are  how  many  ? 

Six  minus  four  are  how  many  ? 

Six  minus  five  are  how  many  ? 

Six  minus  six  are  how  many  ? 


84  FIRST   STEPS    IN   NUMBER. 

Five  and  one  are  how  many  ? 
Four  and  two  are  how  many  ? 
Three  and  three  are  how  many  ? 
Two  and  four  are  how  many  ? 
One  and  five  are  how  many  ? 
Five  and  how  many  are  six  ? 
Four  and  how  many  are  six? 
Three  and  how  many  are  six  ? 
Two  and  how  many  are  six  ? 
One  and  how  many  are  six  ? 
How  many  and  one  are  six? 
How  many  and  two  are  six  ? 
How  many  and  three  are  six? 
How  many  and  four  are  six  ? 
How  many  and  five  are  six  ? 
Three  twos  are  how  many  ? 
Two  threes  are  how  many? 
Six  ones  are  how  many  ? 
How  many  ones  in  six  ? 
How  many  twos  in  six  ? 
How  many  threes  in  six  ? 
How  many  sixes  in  six? 
Count  by  twos  to  six. 
Count  backward  by  twos  from  six. 
Five  are  how  many  more  than  three  ? 
Six  are  how  many  more  than  two  ? 
Two  are  how  many  less  than  five  ? 
Five  are  how  many  less  than  six  ? 
Five  are  how  many  more  than  two  ? 
Four  are  how  many  more  than  one  ? 
One  is  how  many  less  than  six  ? 
Copy: 


'    •  • 

•  •  • 

• 

•  • 

•  •  • 

•  •  •  • 

•  •  • 

•  •  • 

one. 

two. 

tliree. 

four. 

five. 

six. 

THE   NUMBER  SIX.  85 


Pints  in  a  Quart. 

Look  at  these  measures.  (Pint  and  quart  measures.) 
Who  knows  what  this  is  called  ?  what  this  is  called  ? 

Here  is  some  water.  I  will  fill  the  pint  measure,  and  pour 
the  water  into  the  quart  measure.  Does  it  fill  it  ?  I  will 
fill  the  pint  measure  again,  and  pour  the  water  into  the 
quart  measure.     Is  the  quart  measure  full  now? 

How  many  times  did  I  fill  the  pint  measure  ? 

How  many  pints  of  water  does  it  take  to  make  a  quart 
of  water  ? 

Annie  may  find  how  many  pints  it  takes  to  make  a  quart. 

Ned  may  find  how  many  pints  it  takes  to  make  a  quart. 

Susie  may  find  how  many  pints  it  takes  to  make  a  quart. 

How  many  pints  of  water  make  a  quart  of  water  ? 

How  many  pints  of  milk  make  a  quart  of  milk  ? 

How  many  pints  of  molasses  make  a  quart  of  molasses? 

How  many  pints  of  oil  make  a  quart  of  oil  ? 

You  may  write  on  your  slates,  "  Two  pints  of  water  make 
a  quart  of  water." 

If  there  is  a  quart  of  water  in  a  pail,  how  many  pint 
measures  will  it  take  to  hold  the  water  ? 

It  takes  half  a  pint  of  molasses  for  one  loaf  of  ginger- 
bread. I  have  used  a  quart  of  molasses  in  making  ginger- 
bread ;  how  many  loaves  have  I  made  ? 

Mary  drinks  a  half  pint  of  milk  every  morning.  How 
much  will  she  drink  in  four  mornings  ? 

It  takes  a  pint  of  milk  to  make  one  bowl  of  custard.  How 
many  bowls  of  custard  can  I  make  from  a  quart  of  milk  ? 

If  a  quart  of  water  weighs  two  pounds,  how  much  will  a 
pint  of  water  weigh  ? 

If  one  quart  of  berries  costs  six  cents,  what  will  a  pint  of 
berries  cost? 


86  FIRST   STEPS   IN   NUMBER. 

If  a  quart  of  milk  costs  six  cents,  what  will  a  pint  of  milk 
cost  ? 

If  I  pick  a  pint  of  berries  in  half  an  hour,  how  long  will 
it  take  me  to  pick  a  quart  ? 

I  give  my  chickens  a  pint  of  dough  every  morning.  In 
how  many  mornings  shall  I  give  them  a  quart  ? 

If  two  pints  of  peanuts  cost  six  cents,  what  will  a  quart 
of  peanuts  cost  ? 

If  a  quart  of  paint  is  required  to  paint  a  fence,  how  many 
pints  will  it  take  to  paint  the  fence? 

If  a  baker  bakes  a  quart  and  a  half  of  beans  in  a  pot, 
how  many  pints  does  he  bake  in  a  pot? 

How  many  pints  in  three  quarts  ?  in  two  quarts  ? 

In  six  pints  how  many  quarts  ? 

In  five  pints  how  many  quarts,  and  what  part  of  a  quart 
over? 

In  four  pints  how  many  quarts  ? 

In  three  pints  how  many  quarts,  and  what  part  of  a 
quart  over? 

In  one-half  of  six  pints  how  many  quarts,  and  what  part 
of  a  quart  over  ? 

In  one-half  of  four  pints  how  many  quarts  ? 

One-half  of  two  pints  is  what  part  of  a  quart  ? 

Two  halves  of  two  pints  are  how  many  quarts  ? 

If  a  horse  eats  two  and  a  half  quarts  of  corn  for  his  din- 
ner, how  many  pints  of  corn  does  he  eat  ? 

A  two-quart  pail  lacks  one  pint  of  being  full ;  how  many 
pints  are  in  the  pail? 

Two  half-pint  cups  of  water  are  poured  into  a  three-pint 
measure ;  how  many  pints  of  water  will  be  required  to  fill 
the  measure  ? 


CHAPTER  VI. 

THE    NUMBER    SEVEN. 


§  19.   Seven  as  a  Whole. 

Show  me  six  blocks. 

Put  one  more  with  them. 

You  have  shown  me  seven  blocks. 

I  will  show  you  just  as  many  as  you  have  shown  me. 

How  many  do  I  show  you  ? 

Take  six  cards ;  now  take  one  more  card. 

How  many  cards  have  you  ? 

Show  me  seven  fingers ;  seven  pieces  of  paper ;  seven 
blocks  ;  seven  words  on  the  board  ;  seven  ^'s  on  this  slate  ; 
seven  desks ;  seven  panes  of  glass ;  seven  bits  of  crayon  ; 
seven  paper  patterns ;  seven  joints  on  one  hand ;  seven 
buttons  on  your  jacket;  seven  splints. 

Make  seven  dots  on  the  board ;  seven  straight  lines ; 
seven  triangles ;  seven  crosses  ;   seven  squares. 

Who  has  seen  seven  houses?  seven  horses?  seven  per- 
sons? seven  children?  seven  cars?  seven  trees?  seven  steps? 
seven  books?  seven  slates? 

Where  have  you  seen  seven  things,  Annie?  Mary?  Susie? 
Belle  ?  Mamie  ? 

Name  seven  things  in  this  room ;  seven  things  in  the 
parlor  at  home  ;  seven  animals ;  seven  birds  ;  seven  kinds 
of  fruit. 

Copy  the  word  seven. 


88  FIRST   STEPS   IN   NUMBER. 

§  20.   Discoveries  in  Seven. 

•    Who  can  do  something  with  seven  ? 
What  have  you  done  ? 
Who  can  do  something  else  ? 
Tell  me  what  you  have  done. 
Who  can  do  something  else  ? 
Who  can  do  something  else  ? 
What  can  you  take  away  from  seven  ? 
How  many  have  you  left  ? 
What  else  can  you  take  from  seven  ? 
How  many  have  you  left  ? 
What  else  can  you  take  away  from  seven  ? 
How  many  have  you  left  ? 
Arrange  seven  dots  on  the  board,  all  the  ways  you  can. 

Exercise  for  Review. 

Show  me  a  line  an  inch  long. 

Draw  a  square  an  inch  on  each  side. 

Draw  a  figure  on  the  board  having  the  ends  an  inch  in 
length,  and  the  other  sides  two  inches  each  in  length. 

Draw  a  figure  having  six  sid"es,  and  each  side  an  inch 
long. 

Draw  a  square  an  inch  on  each  side,  and  have  a  corner 
point  toward  each  side  of  the  board. 

Draw  a  line  two  inches  long,  and  divide  it  into  halves. 

Draw  a  line  four  inches  long,  and  divide  it  into  halves. 

I  had  several  errands  to  do  this  morning.  I  had  time 
for  only  four,  but  I  shall  do  the  other  two  at  noon.  How 
many  errands  had  I  to  do  in  all  ? 

Nettie  had  several  cents  when  she  started  for  school  this 
morning.  She  spent  four  for  a  sponge,  and  has  three  left. 
How  many  did  she  have  at  first  ? 


THE    NUMBER   SEVEN.  89 

Ned  has  just  so  many  things  to  do  every  morning;  when 
he  has  done  three,  he  can  say,  "Now  I  have  only  three 
more  to  do."  How  many  things  has  ho  to  do  in  the  first 
place  ? 

Willie  drives  the  cows  from  the  pasture  every  night. 
Three  are  usually  at  the  bars,  but  the  other  two  stay  to 
feed.     How  many  has  he  to  drive  home  in  all  ? 

There  was  a  number  of  street-cars  standing  in  a  row ; 
after  four  moved  on,  two  remained.  How  many  were  there 
at  first? 

If  one  log  will  make  four  planks,  how  many  planks  will 
a  log  and  a  half  make  ? 

If  a  driver  hauls  four  loads  of  wood  a  day,  how  many 
loads  will  he  haul  in  a  day  and  a  half? 

If  it  takes  a  yoke  of  oxen  and  a  horse  to  draw  one  load, 
how  many  animals  does  it  take  ? 

If  there  are  three  loads  of  wood  on  the  street,  each  drawn 
by  a  yoke  of  oxen,  how  many  oxen  are  required  to  draw 
the  wood? 

How  many  panes  of  glass  in  a  window  that  has  three 
panes  across,  and  two  up  and  down  ? 

I  divided  six  apples  equally  among  two  boys.  How 
many  apples  did  I  give  to  each  ? 

I  divided  six  cents  among  some  boys,  giving  two  to  each 
boy.     To  how  many  boys  did  I  give  them  ? 

§  21.   Facts  in  Seven. 
Six  and  One. 

Harry  may  give  me  six  watches.  Alice  may  give  me  one 
more  watch.     Who  will  tell  me  how  many  watches  I  have? 

Nellie  may  give  me  six  pitchers.  Arthur  may  give  me 
one  more  pitcher.     How  many  pitchers  do  I  have  ? 

Six  red  rings  and  one  blue  ring  are  how  many  rings? 


90  FIRST  STEPS   IN  NUMBER. 

Point  to  a  group  of  six  stars  on  the  chart.  Point  to  one 
more  star.     To  how  many  stars  have  you  pointed  ? 

Six  IS  and  one  i  are  how  many  zs ? 

Tell  me  a  story  about  six  and  one. 

Tell  me  another  ;  another  ;  another  ;  another  ;  another  ; 
another. 

Write  :  Six  and  one  are  seven. 


One  and  Six. 

Show  me  seven  blocks. 

Show  me  one  of  them  ;  show  me  the  rest.  How  many 
are  there? 

One  block  and  six  blocks  are  how  many  blocks  ? 

One  button  and  six  buttons  are  how  many  buttons  ? 

One  horse  and  six  horses  are  how  many  horses  ? 

One  boy  and  six  boys  are  how  many  boys  ? 

One  picture-book  and  six  picture-books  are  how  many 
picture-books  ? 

Tell  me  a  story  about  one  and  six. 

Exercise  for  Review^. 

I  paid  six  cents  for  a  spool  of  thread  and  a  paper  of  pins. 
The  paper  of  pins  cost  four  cents ;  what  did  the  spool  of 
thread  cost? 

There  were  six  at  table  this  noon,  and  each  had  a  chicken- 
leg.     How  many  chickens  must  there  have  been  ? 

How  many  of  us  might  have  had  a  wing  ? 

If  one  ate  two  wings,  how  many  wings  were  left  for  the 
others  ? 

How  many  wish-bones  were  there  to  distribute  among  us? 

What  part  of  the  number  at  the  table  could  have  wish- 
bones ?  how  many  could  have  a  chance  to  wish  ? 


THE   NUMBER  SEVEN.  91 

Jolm  earns  a  cent  a  day.  Monday  he  finds  he  has  four 
cents  with  the  cent  he  earned  that  day.  On  what  day  will 
he  have  six  cents  ? 

If  he  then  spends  three  cents,  on  what  day  will  he  again 
liave  six  cents? 

If  then  he  buys  two  pencils,  at  two  cents  each,  on  what 
day  will  he  again  have  six  cents  ? 

How  many  more  cents  can  he  earn  that  week? 

A  boy  receives  a  cent  for  every  half-dozen  newspapers 
he  sells.  How  many  half-dozen  newspapers  must  he  sell 
to  earn  six  cents  ?  how  many  dozen  newspapers  ? 

I  bought  two  lemons,  at  two  cents  apiece,  and  gave  a 
five-cent  piece  in  payment.  How  much  money  ought  I  to 
have  received  in  change  ? 

Tell  me  all  the  pairs  of  numbers  which,  put  together,  will 
make  the  number  six ;  all  the  pairs  of  numbers  which,  put 
together,  will  make  the  number  five ;  all  the  pairs  of  num- 
bers that  will  make  the  number  four. 

I  have  one  Christmas-card,  and  Ellen  has  six ;  how  many 
have  we  together? 

I  bought  a  one-cent  stamp  this  morning,  and  two  three- 
cent  stamps  ;  how  much  money  did  I  spend  ? 

If  I  had  bought  two  three-cent  stamps  and  a  one-cent 
stamp,  how  much  should  I  have  spent? 

There  were  three  cows  in  the  pasture ;  one  cow  had  no 
horns.     How  many  horns  did  the  three  cows  have  ? 

A  cow  has  no  upper  front  teeth  ;  how  many  upper  front 
teeth  have  §even  cows  ? 

Annie  has  two  dolls,  and  Mary  four  dolls ;  how  many 
dolls  must  Mary  give  Annie  that  they  may  each  have  the 
same  number  ? 

James  has  three  cents,  and  his  sister  one  cent ;  how  many 
cents  must  James  give  his  sister  that  each  may  have  the 
same  number  of  cents  ? 


92  FIRST  STEPS   m  NUMBER. 

I  have  five  shells,  Ned  has  one ;  how  many  shells  must  I 
give  Ned  that  we  may  each  have  the  same  number  of  shells? 

I  guessed  that  a  package  weighed  four  ounces,  and  Joe 
guessed  it  weighed  three  ounces.  It  weighed  three  ouncei? 
and  a  half.    Which  made  the  better  guess  ? 

Seven  minus  One. 

Who  will  find  seven  things  on  the  table  first? 

Do  as  I  do.     (I  put  one  under  the  table.) 

How  many  have  you  taken  away  ? 

How  many  have  you  left  on  the  table  ? 

Tell  me  a  story  about  this. 

Tell  me  another  story  about  this ;  another ;  another ; 
another. 

If  there  are  seven  men  walking  along  the  street,  and  one 
loses  his  hat,  how  many  men  have  hats  on  ? 

If  you  have  seven  paper  dolls,  and  one  is  swept  into  the 
fire,  how  many  will  you  then  have? 

Annie  owned  seven  doves,  but  one  died ;  how  many  did 
she  then  have  ? 

There  are  seven  cattle  in  the  pasture ;  one  of  them  is 
lying  down,  the  rest  are  feeding.     How  many  are  feeding  ? 

Exercise  for  Review. 

Read  what  I  show  you  with  the  blocks. 

Bead  what  I  show  you  with  the  dots  on  the  toard. 

Ed  had  six  hens,  but  sold  half  of  them ;  how  many  did 
ne  have  left  ? 

After  Nettie  had  spent  half  her  money,  she  had  three 
cents ;  how  much  did  she  have  at  first  ? 

After  Willie  had  copied  three  words,  he  had  just  as 
many  more  to  copy ;  how  many  did  he  have  to  copy  in  all? 


THE   NUMBER  SEVEN.  93 

After  Lizzie  had  copied  two  words,  she  had  twice  as 
many  more  to  copy  ;  how  many  words  did  she  have  to  copy 
altogether  ? 

Mary  has  six  words  to  learn,  Jane  four  words ;  how 
many  more  words  has  Mary  to  learn  than  Jane  ? 

One-half  of  six  is  how  many  more  than  one-half  of  four  ? 

One-half  of  four  is  how  many  more  than  one-half  of  two  ? 

One-half  of  six  is  how  many  more  than  one-half  of  two  ? 

I  guessed  it  took  six  hours  to  go  to  New  York,  and 
George  guessed  it  took  four  hours.  Neither  was  right,  but 
one  was  just  as  nearly  right  aS  the  other ;  how  many  hours 
did  it  take  ? 

After  John  had  brought  in  one  armful  of  wood,  he  had 
three  times  as  many  more  to  bring  in ;  how  many  armfuls 
did  he  have  to  bring  in  at  first  ? 

Ruth  has  a  strip  of  paper  six  inches  long  which  she  wishes 
to  cut  into  strips  two  inches  long.  How  many  times  must 
she  cut  the  paper  ?     How  many  strips  will  she  have  ? 

Seven  minus  Six. 

Take  seven  blocks.  Put  six  under  the  table.  What 
have  you  left  on  the  table  ? 

I  had  seven  children  with  their  hands  under  the  table  a 
moment  ago ;  now  six  of  them  have  their  hands  on  the  table; 
how  many  have  hands  under  the  table  ? 

There  are  seven  days  in  a  week ;  we  work  six  days ;  how 
many  days  have  we  for  rest  ? 

There  are  seven  windows  on  the  side  of  a  house ;  six  are 
arranged  in  pairs ;  how  many  are  there  besides  the  six 
arranged  in  pairs  ? 

If  Mary  bought  three  pears,  at  two  cents  each,  and  gave 
in  payment  for  them  a  five-cent  piece  and  a  two-cent  }ueoe, 
how  much  money  should  she  receive  back? 

Tell  me  a  story  about  seven  minus  six. 


94 


FIEST   STEPS   IN   NUMBER. 


Exercise  for  Review. 

Tell  the  number  of  dots  as  I  point. 


• 

• 

•      • 

— 

— 

•  • 
•  • 

• 

•  •  •  • 

• 
•  •  • 

• 
•  •  • 

•  •  • 
• 

• 

•  • 
• 

• 

• 

• 

•     • 

•     • 

• 

•  • 

•  • 

•    • 
• 

•  • 

•  •  • 
• 

•  •  • 

• 

•  • 

•  •  • 

•  • 
•       • 

••• 

• 

•  •• 

• 
• 

•• 

• 

• 

• 

• 

• 

•  • 

•     • 

•  i 

1  • 

• 

•• 

•• 

•  • 

• 

•  • 

• 
•     • 

• 

• 

Make  an  example  for  what  I  show  you  with  the  blocks. 

Mary  may  give  examples  for  the  class. 

I  have  a  ball  which  is  two  inches  through  ;  if  it  is  three 
times  as  far  round  the  ball,  how  large  round  is  the  ball  ? 

On  Nellie's  sixth  birthday  she  had  six  little  girls  to  tea ; 
how  many  little  girls  were  there  then  ? 

If  she  is  six  years  old  now,  how  old  will  she  be  a  year 
from  now  ?  How  old  was  she  her  last  birthday  ?  How 
many  years  ago  was  she  half  as  old  as  she  is  now? 

If  a  train  moves  a  mile  in  two  minutes,  how  many  miles 
will  it  move  in  six  minutes?  what  part  of  a  mile  in  one 
minute  ? 

If  a  horse  is  five  years  old,  in  how  many  years  will  he  be 
six  years  old  ? 

If  Maggie  picks  a  pint  of  berries  a  day,  how  many  quarts 
of  berries  will  she  pick  in  a  week  ? 


THE  NUMBER  SEVEN.  95 


Five  and  Two. 


Take  seven  blocks.     Put  them  in  groups  of  five  and  two. 

Five  blocks  and  two  blocks  are  how  many  blocks  ? 

One  of  two  girls  had  five  books,  the  other  had  two ;  how 
many  books  had  they  together  ? 

John  had  five  brown  rabbits  and  two  white  ones  ;  how 
many  rabbits  had  he  ? 

A  little  boy  going  to  school  met  five  of  his  playmates, 
who  walked  to  school  with  him  ;  on  their  way  they  met  two 
of  their  classmates  going  fishing.  How  many  of  his  school- 
mates did  the  boy  meet  ? 

Annie  was  to  have  a  birthday  party  ;  she  had  two  sisters, 
and  her  mother  told  her  she  might  invite  five  of  her  friends. 
How  many  were  there  at  the  party  beside  herself? 

Some  boys  coasting  down  hill  had  fastened  five  sleds  to- 
gether, when  two  more  boys  came  along  each  with  a  sled  ; 
when  these  were  joined,  with  how  many  sleds  did  they  start 
down  hill? 

Frank's  mother  wished  him  to  do  an  errand  for  her ; 
before  he  could  go,  he  had  to  find  his  hat,  which  took  five 
minutes,  and  his  mittens,  which  took  two  minutes  more. 
How  long  before  he  was  ready  to  do  his  errand? 

Frank  made  five  sail-boats  for  his  sister,  but  as  part  of 
them  were  lost  in  sailing,  she  got  him  to  make  her  two 
more,  without  sails  ;  how  many  boats  in  all  did  Frank 
make? 

George  played  ball  a  certain  number  of  times ;  his  side 
was  beaten  five  times,  and  the  other  side  was  beaten  by  his 
two  times ;  how  many  games  did  he  play  in  all  ? 

A  boy  was  sent  to  pick  a  pailful  of  plums ;  wishing  to 
show  how  many  he  had  picked,  he  turned  them  into  two 
measures,  which  just  held  them,  one  containing  five  quarts, 
the  other  two  quarts.     How  many  quarts  did  he  pick  ? 


96  FIRST  STEPS   IN   NUMBER. 


Exercise  for  Review. 


If  Harry  gives  me  one  cent,  Mary  gives  me  two  cents, ' 
Jamie  gives  me  three  cents,  and  Nellie  one  cent,  how  many 
cents  will  I  have  ? 

Two  pencils  and  three  pencils  and  two  more  pencils  are 
how  many  pencils  ? 

Five  birds  are  in  a  tree ;  two  birds  fly  away,  then  three 
birds  fly  away  ;  and  then  four  birds  fly  into  the  tree.  How 
many  birds  are  in  the  tree  ? 

Seven  crows  were  on  the  ground  ;  one  of  them  flew  away, 
and  four  flew  into  a  tree  ;  afterwards  two  of  the  four  crows 
flew  down  upon  the  ground,  and  then  the  other  two  flew 
down.     How  many  were  on  the  ground  then  ? 

Write  what  I  show  you.  (Have  the  operation  which  is 
shown  expressed  in  words,  on  board  or  slate,  thus  :  One  and 
two  are  three  ;  Four  minus  one  are  three.) 

In  a  class  of  seven  children  there  is  only  one  girl;  how 
many  are  boys  ? 

If  two  boys  and  two  girls  and  two  dogs  are  running  in 
the  field,  how  many  are  running  in  the  field  ? 

On  one  twig  there  were  five  cherries,  and  on  another  two 
cherries;  how  many  cherries  were  on  both  twigs? 

If  one-half  of  four  sheep  have  two  lambs  each,  and  the 
other  half  have  one  lamb  each,  how  many  lambs  are  there 
in  all? 

Two  and  Five. 

George  has  two  marbles,  and  John  has  five  marbles  ;  how 
many  marbles  have  both  ? 

Annie  has  two  apples,  and  Susie  has  five  apples ;  how 
many  apples  have  both  ? 

John  went  fishing  twice  last  week.  The  first  time  he 
caught  only  two  fish,  but  the  next  time  he  caught  five  ;  how 
many  fish  did  he  catch  in  all  ? 


THE   NUMBER  SEVEN.     .  97 

Yesterday  Annie's  aunt  gave  her  two  cents,  and  her 
uncle  gave  her  five  cents ;  how  much  money  had  she  then  ? 

George  sawed  two  sticks  of  wood  this  morning,  and  five 
more  this  afternoon ;  how  many  sticks  of  wood  did  he 
saw? 

In  my  new  picture-book  there  is  a  picture  of  two  kittens 
running  after  a  ball,  and  fiye  more  asleep  on  a  rug;  how 
many  kittens  are  there  in  all  ? 

The  other  morning  Addie  saw  two  birds  in  one  tree,  and 
five  in  another ;  how  many  birds  did  she  see  in  all  ? 

There  are  two  blocks  on  my  desk,  and  ^ve  blocks  on 
Susie's ;  how  many  blocks  are  there  in  all  ? 

Exercise  for  Review. 

Tf  a  little  house-fly  should  lose  four  of  its  legs,  how  many 
legs  would  it  then  have? 

I  have  a  little  paper  measure  which  is  six  inches  long ; 
if  I  cut  off  two  inches,  how  long  will  it  be  ? 

Addie  has  six  splints  with  which  to  make  figures  to-day; 
yesterday  I  gave  her  but  four;  how  many  more  has  she 
to-day  ? 

Six  children  were  drawing  on  the  board,  but  two  have 
takeli  their  seats;  how  many  remain  at  the  board? 

How  many  quarts  will  a  six-pint  pail  contain  ? 

How  many  pairs  of  legs  has  a  house-fly  ? 

How  many  legs  has  he  on  a  side  ? 

If  there  were  five  boys  skating  on  the  pond,  and  two 
more  came  to  join  them,  how  many  boys  would  be  on  the 
pond? 

If  George,  in  skating,  fell  down  five  times,  and  then  two 
times  more,  how  many  times  did  he  fall  down  ? 

I  have  a  five-cent  piece  and  a  two-cent  piece ;  how  much 
money  have  I  ? 


98  FIRST  STEPS   IN   NUMBER. 

I  have  a  three-cent  piece,  a  two-cent  piece,  and  one  cent ; 
how  much  money  have  I  ? 

If  I  owe  you  seven  cents,  and  pay  you  in  two-cent  pieces, 
as  far  as  I  can,  what  else  must  I  give  you?  How  many 
two-cent  pieces  do  I  pay  you  ? 

If  I  owe  you  six  cents,  and  give  you  three  pieces  of 
money  in  payment,  what  can  the  pieces  of  money  be? 
What  else  can  the  pieces  of  money  be? 

If  I  paid  you  with  two  pieces  of  money,  what  could  the 
pieces  be  ?     What  else  could  the  pieces  be  ? 

If  I  paid  you  with  six  pieces  of  money,  what  would  the 
pieces  be  ?  If  I  paid  you  with  five  pieces  of  money  ?  If  I 
paid  you  with  four  pieces  of  money  ? 

Three  two-cent  pieces  are  how^  much  money  ? 

A  three-cent  piece,  a  two-cent  piece,  and  one  cent  are 
how  much  money  ? 

Two  three-cent  pieces  are  how  much  money  ? 

A  five-cent  piece  and  one  cent  are  how  much  money  ? 

A  two-cent  piece  and  four  cents  are  how  much  money  ? 

A  three-cent  piece  and  three  cents  are  how  much  money? 


Seven  minus  Two. 

Ned  had  seven  fish-hooks,  but  lost  two ;  how  many  had 
he  left? 

It  rained  two  days  last  week;  how  many  days  were 
pleasant  ? 

Seven  cousins  were  invited  to  a  picnic ;  two  could  not 
go.     How  many  went? 

If  I  have  seven  nuts,  and  crack  two,  how  many  whole 
nuts  have  I  then  ? 

If  I  make  seven  snow-balls,  and  throw  two,  how  many 
have  I  left? 


THE   NUMBER  SEVEN.  99 

The  cook  lias  seven  pies  in  the  oven.  If  she  takes  out 
two,  how  many  will  be  left  in  the  oven  ? 

There  were  seven  pins  on  the  carpet.  Susie  picked  up 
two.     How  many  pins  were  left  on  the  carpet? 

Uncle  Ned  had  seven  pennies  in  his  pocket.  He  gave 
two  to  Willie.     How  many  had  he  left  ? 

There  were  seven  apples  on  one  branch ;  two  fell  off. 
How  many  were  left  on  the  branch  ? 

Ned  was  at  home  only  two  days  last  week ;  how  many 
days  was  he  away  ? 

There  are  seven  lamps  in  a  room ;  two  are  not  lighted. 
How  many  are  lighted  ? 

There  are  seven  sleighs  on  the  street ;  two  have  no  bells. 
How  many  have  bells  ? 

You  may  tell  me  a  story  about  seven  minus  two. 

Write  on  your  slate :  Seven  minus  two  are  five. 

Illustrate  in  all  the  ways  you  can  that  seven  minus  two 
are  five,  by  drawings  on  your  slate. 

Exercise  for  Review. 

Tell  the  number  of  dots  as  I  point.     (See  p.  94.) 

Make  an  example  for  what  I  show  you.      (See  p.  61.) 

I  will  give  you  examples,  and  you  may  show  me  what  is 
meant. 

Write  on  your  slate  what  I  show  you.  (This  is  just  the 
same  as  the  reading,  only  the  fact  is  written  instead  of 
spoken.) 

Read  what  you  have  written. 

Name  all  the  numbers  less  than  seven. 

Name  a  number  that  is  three  more  than  two ;  that  is 
three  more  than  three ;  three  more  than  one. 

Name  a  number  that  is  two  more  than  four ;  that  is  two 
more  than  fiYQ  ;  two  more  than  three  ;  two  more  than  one. 


100  FIRST  STEPS   IN   NUMBEK. 

Name  a  number  that  is  four  more  than  two ;  four  more 
than  one. 

Three  and  three  are  how  many  ? 

Two  and  two  are  how  many  ? 

If  half  of  six  blocks  are  taken  away,  what  part  of  the  six 
blocks  will  be  left? 

Name  a  number  that  is  two  less  than  six ;  two  less  than 
five;  two  less  than  seven. 

Name  a  number  that  is  three  less  than  five  ;  three  less 
than  four  ;  three  less  than  six. 


Seven  minus  Five. 

Paul  caught  seven  butterflies,  but  let  five  fly  away  ;  how 
many  butterflies  had  he  left? 

Johnny  goes  to  school  five  days  in  the  week ;  how  many 
days  does  he  stay  at  home  ? 

Tom  picked  seven  quarts  of  blueberries,  but  sold  five 
quarts ;  how  many  had  he  left  ? 

Mary  has  seven  brothers  and  sisters.  She  has  five  broth- 
ers ;  how  many  sisters  has  she  ? 

Minnie's  geranium  had  seven  blossoms,  but  she  picked 
five ;  how  many  blossoms  had  she  left  ? 

Susie  had  seven  paper  dolls,  but  her  baby  brother  spoiled 
five ;  how  many  paper  dolls  had  she  left  ? 

Tim  had  seven  oranges,  but  gave  away  five ;  how  many 
oranges  had  he  left  ? 

Charlie  goes  seven  miles  to  see  his  grandmother.  He 
rides  five  miles,  and  walks  the  rest  of  the  way ;  how  many 
miles  does  he  walk  ? 

Mattie  had  seven  birthday  and  Christmas  cards.  Five 
were  Christmas  cards ;  how  many  were  birthday  cards  ? 

Seven  kittens  are  playing  in  the  yard.  Five  are  gray, 
and  the  rest  white  ;  how  many  are  white  ? 


THE   NUMBER  SEVEN.  101 


The  Gill. 


Who  has  seen  a  little  cup  like  this  at  home  ? 

Who  has  seen  a  little  cup  like  this  at  the  tin-shop  ? 

What  do  you  call  such  a  cup  ? 

Who  ever  picked  a  gill  of  berries  ?  bought  a  gill  of  pea- 
nuts ?  drank  a  gill  of  water  at  one  time  ?  bought  a  gill  of 
yeast  at  the  baker's  ? 

You  may  write  the  word  gill  on  your  slate. 

Look  at  this.  (Pint  measure.)  What  do  you  call  it? 
Which  will  hold  more,  the  gill  or  the  pint  measure  ? 

For  which  will  you  have  to  pay  more,  for  a  gill  of  nuts 
or  for  a  pint  of  nuts  ?  for  a  gill  of  milk  or  for  a  pint  of 
milk  ?  for  a  gill  of  vinegar  or  for  a  pint  of  vinegar  ? 

Gills  in  a  Pint. 

Nettie  may  fill  the  gill  cup  with  water.  Pour  it  into  the 
pint  measure.     Is  the  pint  measure  full  ? 

Put  another  gill  of  water  in  the  measure. 

How  many  gills  are  in  the  measure  now  ?     Is  it  full  ? 

Put  another  gill  in  the  measure. 

How  many  gills  does  it  take  to  fill  the  pint  measure  ? 

Johnny  may  measure  and  see  if  it  takes  four  gills  of 
water  to  make  a  pint  of  water. 

In  a  pint  of  milk  how  many  gills  of  milk  ? 

In  a  pint  of  vinegar  how  many  gills  of  vinegar? 

In  a  pint  of  yeast  how  many  gills  of  yeast? 

In  a  pint  of  molasses  how  many,  gills  of  molasses  ? 

Johnny  picks  berries  in  a  gill  cup ;  how  many  times 
must  he  fill  it  to  have  a  pint  of  berries  ? 

If  your  mother  uses  a  gill  of  yeast  each  time  she  makes 
bread,  how  many  times  can  she  make  bread  from  a  pint  of 
yeast  ? 


102  FIRST  STEPS   IN   NUMBER. 

If  it  takes  two  gills  of  molasses  to  make  a  loaf  of  ginger- 
bread, how  many  loaves  can  be  made  from  a  pint  of 
molasses  ? 

A  cofFee-cup  holds  half  a  pint ;  how  many  gills  does  it 
hold? 

A  saucer  holds  half  a  pint ;  how  many  gills  does  a  saucer 
hold? 

I  have  a  mug  which  holds  half  a  pint ;  how  many  gills 
does  it  hold  ? 

Two  gills  are  what  part  of  a  pint  ? 

If  I  put  two  gills  of  water  in  a  pint  measure,  how  near 
full  is  it? 

If  there  is  only  one  gill  of  milk  in  a  pint  measure,  how 
many  more  gills  can  I  put  in  it  before  it  is  full  ? 

You  may  write  on  your  slates  :  Four  gills  make  one  pint. 

Exercise  for  Review. 

If  one  spool  of  thread  costs  two  cents,  what  will  three 
spools  cost? 

If  I  have  seven  cents,  how  many  cents  shall  I  have  left 
after  paying  for  the  three  spools  of  thread  ? 

In  a  group  of  seven  stars  two  are  so  faint  that  I  ear- 
scarcely  see  them ;  how  many  can  I  see  plainly  ? 

Seven  children  are  busy  at  the  table.  Five  are  building 
block-houses,  and  the  rest  are  laying  sticks  ;  how  many  are 
laying  sticks  ? 

Those  who  were  laying  sticks,  and  three  of  the  others, 
have  gone  to  their  desks ;  how  many  remain  at  the  table  ? 

The  two  who  remained  at  the  table,  and  four  others, 
have  now  gone  to  the  board  to  draw ;  how  many  are  draw- 
ing at  the  board  ? 

In  two  years  more  Nellie  will  be  seven  years  old,  and 
Jessie  five ;  how  much  older  is  Nellie  than  Jessie  now  ? 


THE   NUMBER  SEVEN.  103 

Four  and  Three. 

Katie  made  four  fans,  and  Jessie  made  three  ;  how  many- 
did  they  both  make  ? 

Harry  caught  four  trout,  and  Tom  caught  three;  how 
many  did  both  catch  ? 

Jamie  had  four  bunches  of  grapes,  and  picked  three 
bunches ;  how  many  bunches  had  he  then  ? 

Annie  has  four  yards  of  ribbon,  and  Mary  has  three ; 
how  many  yards  of  ribbon  have  they  together  ? 

Charlie's  father  has  four  horses,  and  Lena's  father  has 
three  ;  how  many  horses  have  both  ? 

Johnny  picked  four  cherries  and  afterwards  three  cher- 
ries ;  how  many  cherries  did  he  pick  in  all  ? 

Susie  swept  four  rooms,  and  Rose  swept  three  rooms ; 
how  many  rooms  did  they  sweep  in  all  ? 

Frank  skated  four  miles  Wednesday  and  three  miles 
Thursday ;  how  many  miles  did  he  skate  in  all  ? 

Ned  found  four  eggs  in  the  barn,  and  Isaac  three;  how 
many  eggs  did  they  find  together  ? 

Three  dogs  were  chasing  four  foxes ;  how  many  animals 
were  running? 

Fanny  cut  out  four  cookies,  and  Belle  cut  out  three ; 
how  many  cookies  did  both  cut  out  ? 

Joe  rolled  four  marbles,  and  George  rolled  three ;  how 
many  marbles  did  both  roll  ? 

Exercise  for  Review. 

If  Mary  has  five  cents,  and  I  have  two,  and  Mary  gives 
me  one  cent,  how  many  cents  will  each  have  ? 

If  Louis  has  seven  cents,  and  I  five,  and  Louis  gives  me 
one  cent,  how  many  cents  will  each  have  ? 

If  two  men  are  six  miles  apart,  and  each  walks  toward 
the  other  two  miles,  how  many  miles  are  they  apart  then? 


104  FIRST  STEPS   IN  NUMBER. 

Ina  has  seven  cents,  Ellen  five.  Jennie  has  more  than 
Ellen  and  less  than  Ina.     How  many  cents  has  Jennie  ? 

In  a  bird's  nest  there  are  seven  birds ;  five  are  little 
birds,  the  rest  are  old  birds ;  how  many  are  old  birds  ? 

Kittie  has  seven  cousins,  and  Ralph  has  five ;  how  many 
more  cousins  has  Kittie  than  Ralph  ? 

Mamie  has  seven  dolls,  but  Charlie  has  hidden  five  ;  how 
many  has  Mamie  to  play  with  ? 

If  Albert  throws  four  snow-balls,  and  Cyrus  throws  three, 
how  many  snow-balls  do  both  throw  ? 

Write  on  your  slates  the  word  that  stands  for  the  num- 
ber which  I  show  you. 

Mary  picked  four  quarts  of  blueberries,  and  Lucy  three ; 
how  many  did  both  pick  ? 

What  will  a  quart  of  milk  cost  at  three  cents  a  pint  ? 

What  will  a  quart  and  a  half  of  milk  cost  at  two  cents 
a  pint  ? 

If  a  gill  of  peanuts  cost  two  cents,  what  will  half  a  pint 
of  peanuts  cost  ? 

If  half  a  pint  of  syrup  cost  six  cents,  what  will  a  gill  of 
syrup  cost? 

George  earns  two  cents  every  other  day  in  the  week,  and 
Harry  earns  one  cent  every  day.  Which  earns  the  more 
money  in  a  week  ? 

There  is  a  group  of  stars  called  the  dipper ;  four  stars 
form  the  handle  and  three  others  the  cup  ;  how  many  stars 
are  there  in  the  dipper  ? 

If  there  were  four  showers  last  week,  and  three  this 
week,  how  many  showers  were  there  in  all  ? 

Divide  seven  into  two  such  groups  that  there  will  be  one 
more  in  one  group  than  in  the  other  group. 

Divide  seven  into  three  such  groups  that  one  will  be 
larger  by  one  than  either  of  the  other  groups. 


THE  NUMBER  SEVEN.  105 

Three  and  Four. 

A  hen  has  three  white  chickens  and  four  black  chickens; 
how  many  has  she  in  all  ? 

If  I  have  three  nuts,  and  Johnny  gives  me  four,  how 
many  nuts  have  I  then  ? 

Charlie  brings  in  three  armfuls  of  wood,  and  Bertie 
brings  in  four ;  how  many  do  both  bring  in  ? 

If  there  are  three  boys  skating  on  the  pond,  and  four 
more  come  to  join  them,  how  many  are  then  skating? 

If  three  boys  are  riding  on  a  sled,  and  four  more  jump 
on,  how  many  are  then  on  the  sled  ? 

If  Katie  slides  down  hill  three  times  in  the  morning,  an(J 
four  times  in  the  afternoon,  how  many  times  does  she  slide 
down  hill  ? 

Susie  found  a  nest  with  three  eggs  in  it,  and  Amy  a  nest 
with  four  eggs  in  it ;  how  many  eggs  did  both  find  ? 

If  I  ascend  three  rounds  of  the  ladder,  and  there  are  four 
more  to  ascend,  how  many  rounds  has  the  ladder  ? 

Exercise  for  Review. 

Seven  minus  six  are  how  many  ? 
Seven  minus  what  number  leaves  one  ? 
What  number  minus  six  leaves  one  ? 
Seven  minus  five  are  how  many  ? 
Seven  minus  what  number  leaves  two  ? 
What  number  minus  five  leaves  two  ? 
Seven  minus  two  are  how  many  ? 
Seven  minus  what  number  leaves  five  ? 
What  number  minus  two  leaves  five  ? 
Two  and  five  are  how  many  ? 
Five  and  two  are  how  many  ? 
Two  and  what  number  are  seven  ? 


106  FIRST  STEPS   IN   NUMBER. 

Five  and  what  number  are  seven  ? 
What  number  and  two  are  seven  ? 
What  number  and  five  are  seven  ? 
Four  and  three  are  how  many? 
Four  and  what  number  are  seven  ? 
What  number  and  three  are  seven  ? 
Three  and  four  are  how  many  ? 
Three  and  what  number  are  seven  ? 
What  number  and  four  are  seven  ? 


Seven  minus  Three. 

There  were  seven  rolls  on  the  plate ;  after  three  were 
taken  how  many  remained  ? 

Nellie  is  knitting  a  wrister ;  she  knits  seven  times  round 
it  every  day  ;  when  she  has  knit  round  it  three  times  how 
many  more  times  has  she  to  knit  round  it? 

I  am  at  home  three  days  in  the  week ;  how  many  days 
am  I  away  from  home  ? 

We  have  seven  weeks'  vacation  in  the  summer ;  if  I  work 
three  weeks,  how  many  weeks  have  I  for  rest  ? 

If  Ralph  must  learn  to  spell  seven  words,  and  has  learned 
to  spell  three,  how  many  more  has  he  to  learn  to  spell? 

If  you  have  seven  cups  and  saucers  to  wipe,  and  have 
wiped  three  cups  and  saucers,  how  many  more  must  you 
wipe  ? 

Seven  children  were  making  clay  balls ;  three  have  their 
balls  made ;  how  many  are  still  making  clay  balls  ? 

Seven  children  are  working  in  clay ;  three  are  making 
cubes,  and  the  rest  are  making  cylinders.  How  many  are 
making  cylinders  ? 

It  rained  three  days  last  week.  How  many  days  were 
pleasant  ? 

Copy  :    Seven  minus  three  are  four. 


THE   NUMBER  SEVEN.  107 


Seven  minus  Four. 

If  it  is  seven  miles  to  a  certain  lake,  and  I  have  trav- 
elled four  miles,  how  much  farther  must  I  travel  before  I 
reach  the  lake  ? 

If  there  are  seven  cows  in  a  pasture,  and  four  are  driven 
out,  how  many  will  remain  in  the  pasture  ? 

If  it  takes  seven  yards  of  velvet  to  make  my  dress,  and 
four  yards  to  make  yours,  how  many  more  does  it  require 
for  my  dress  ? 

I  have  seven  cents.  If  I  spend  four  cents  for  a  bunch 
of  envelopes,  how  many  cents  will  be  left  ? 

I  gave  seven  little  boys  some  number  work  to  do ;  four 
have  their  work  done.     How  many  are  still  working? 

If  there  were  seven  boys  playing  ball,  and  four  left  the 
game,  how  many  were  left  to  continue  the  game  ? 

Show  me  on  the  board  that  seven  dots  minus  four  dots 
are  three  dots. 

Show  me  that  seven  straight  lines  minus  four  straight 
lines  are  three  straight  lines. 

Write  :  Seven  minus  four  are  three. 


Exercise  for  Review. 

Two  pencils,  three  pencils,  one  pencil,  and  one  pencil  are 
how  many  pencils? 

Three  sheep,  two  sheep,  and  two  sheep  are  how  many 
sheep  ? 

Four  chickens  and  three  chickens  are  how  many  chick- 
ens? 

A  figure  of  patch-work  had  two  pieces  on  each  of  two 
sides,  and  one  piece  on  each  of  the  other  two  sides ;  how 
many  pieces  did  the  figure  contain  ? 


108  FIRST   STEPS   IN   NUMBER. 

We  have  in  our  barn  two  old  cats  and  five  kittens ;  liow 
many  cats  and.ldttens  have  we  in  all? 

If  there  are  three  mugs  on  the  table,  and  I  put  four 
more  on  the  table,  how  many  mugs  will  be  on  the  table  ? 

If  only  three  of  these  mugs  have  milk  in  them,  how 
many  do  not  have  milk  in  them  ? 

If  I  have  seven  little  fans,  and  give  you  four,  how  many 
fans  shall  I  have  left  ? 

If  I  have  seven  letters  to  write,  and  I  write  three,  how 
many  more  shall  I  have  to  write  ? 

How  many  strokes  does  the  clock  strike  between  half- 
past  twelve  and  half-past  three  ? 

I  have  a  book  which  has  as  many  leaves  as  there  are 
days  in  the  week  less  one ;  how  many  leaves  has  it  ? 

How  many  pairs  of  skates  and  how  many  odd  skates 
have  you  if  you  have  seven  skates  ? 

How  many  pairs  of  gloves  and  how  many  odd  gloves 
have  you  if  you  have  seven  gloves  ? 

How  many  boots  will  there  be  in  three  pairs  of  boots 
and  one  odd  boot  ? 

If  Jamie  has  seven  yards  of  line  to  his  kite,  and  John 
has  two  yards  in  one  piece  of  his  line,  three  in  another 
piece,  and  one  yard  in  each  of  two  other  pieces  of  his  line, 
who  has  the  longer  line  to  his  kite  ? 

Which  is  more  money,  a  five-cent  piece  and  a  two-cent 
piece ;  or,  a  three-cent  piece,  a  two-cent  piece,  and  two  cents? 

Which  cost  more,  two  books  at  three  dollars  each,  and 
one  book  at  one  dollar ;  or,  three  books  at  two  dollars  each, 
and  two  books  at  a  half-dollar  each  ? 

If  it  takes  two  yards  and  a  half  of  cloth  to  make  a  jacket, 
how  much  cloth  will  it  take  for  two  jackets? 

If  a  confectioner  uses  three  ounces  and  a  half  of  chocolate 
for  one  lot  of  taffy,  how  many  ounces  will  he  use  for  two 
such  lots  ? 


THE   NUMBER  SEVEN.  109 

If  two  quarts  of  maple  syrup  will  make  three  pounds  of 
sugar,  what  will  a  quart  of  maple  syrup  make  ? 

If  two  cakes  of  maple  sugar  weigh  together  a  pound, 
what  part  of  a  pound  will  one  cake  weigh  ? 

How  many  pounds  will  four  cakes  weigh  ? 

How  many  pounds  will  six  cakes  weigh  ? 

What  will  seven  cakes  weigh  ? 

How  many  cakes  that  weigh  a  half  a  pound  each  will  it 
take  to  equal  three  cakes  that  weigh  a  pound  each? 

If  half  a  pint  of  syrup  makes  half  a  pound  of  sugar,  what 
will  four  gills  of  syrup  make  ? 

If  the  cars  pass  our  house  every  half-hour,  how  many 
times  will  they  pass  the  house  in  three  hours  and  a  half? 

Name  two  numbers  which  together  make  seven. 

Name  all  the  two  numbers  which  together  make  seven. 

Three  and  three  and  how  many  are  seven  ? 

Two  and  three  and  how  many  are  seven  ? 

One  and  three  and  how  many  are  seven  ? 

Three  and  how  many  are  seven  ? 

Four  and  how  many  are  seven  ? 

Two  and  how  many  are  seven  ? 

Seven  minus  two  minus  four  are  how  many  ? 

Seven  minus  three  minus  two  are  how  many  ? 

Seven  minus  two  minus  two  are  how  many  ? 

Seven  minus  one  minus  two  are  how  many  ? 

Seven  minus  two  are  how  many  ? 


Seven  minus  Seven. 

Johnny  had  seven  marbles,  but  on  his  way  to  school  he 
lost  seven  of  them ;  how  many  had  he  left  ? 

There  were  seven  eggs  in  a  nest,  but  seven  of  them  got 
broken ;  how  many  were  there  left  in  the  nest  ? 


110  FIEST   STEPS   IN   NUMBER. 

Minnie  had  seven  paper  dolls,  but  gave  seven  of  them  to 
her  little  sister  ;,  how  many  had  she  then  ? 

In  the  school-yard  there  are  seven  boys  playing  ball,  and 
seven  playing  marbles ;  how  many  more  boys  are  playing 
ball  than  are  playing  marbles  ? 

Harry  made  seven  snow  men,  but  seven  of  them  melted 
away  ;  how  many  were  left  ? 

George  had  seven  rabbits,  but  seven  of  them  got  away ; 
how  many  had  he  then  ? 

Fannie's  uncle  gave  her  seven  pet  doves,  but  seven  of 
them  were  sick  and  died  ;  how  many  had  she  then  ? 

There  were  seven  mice  playing  in  the  cellar ;  the  old  cat 
caught  seven  of  them  ;  how  many  mice  were  left  playing 
in  the  cellar? 

In  a  doll-carriage  seven  dolls  were  riding,  but  seven  of 
them  were  tipped  out;  how  many  were  left  in  the  carriage? 

Seven  robins  were  singing  in  a  tree ;  a  boy  threw  a  stone 
and  frightened  seven  of  them  away  ;  how  many  robins  were 
left  singing  in  the  tree  ? 

Copy  :    Seven  minus  seven  is  none. 

Seven  divided  by  One. 

Take  seven  blocks.  Show  me  one  of  your  seven  blocks. 
Show  me  another  ;  another  ;  another  ;  another  ;  another  ; 
another. 

How  many  one-blocks  in  your  seven  blocks  ? 

If  there  were  seven  oranges  here,  how  many  of  us  could 
have  one  apiece? 

Seven  lamp-chimneys  will  supply  how  many  lamps  ? 

Seven  lamp-shades  will  supply  how  many  lamps  ? 

Seven  slates  will  supply  hoAV  many  children  ? 

I  have  seven  hanging-pots  of  flowers ;  if  I  hang  one  at  a 
window,  at  how  many  windows  can  I  hang  them  ? 


THE   NUMBER  SEVEN.  HI 

I  have  seven  brackets  ;  if  I  put  each  on  a  hook  by  itself, 
how  many  hooks  will  it  take  ? 

I  have  seven  bottles  to  pack ;  it  takes  a  box  for  each 
bottle  ;  how  many  boxes  must  I  have  ? 

Write :    There  are  seven  ones  in  seven. 

Seven  Ones. 

How  many  heads  have  seven  boys  ? 

How  many  hats  will  seven  boys  need  ? 

If  I  read  a  book  every  day,  how  many  books  shall  I  read 
in  a  week  ?  , 

If  I  read  an  hour  each  day,  how  many  hours  shall  I  read 
in  a  week  ? 

If  a  bottle  of  ink  lasts  me  a  year,  how  many  bottles  shall 
I  use  in  seven  years  ? 

If  a  family  uses  a  barrel  of  flour  a  month,  how  many 
barrels  will  they  use  in  seven  months  ? 

If  I  must  wind  my  watch  once  a  day,  how  many  times 
must  I  wind  it  in  a  week  ? 

If  my  watch  loses  a  second  a  day,  how  many  seconds 
will  it  lose  in  a  week  ? 

If  you  put  a  cent  in  the  box  every  Sunday,  how  many 
cents  will  you  put  in  in  seven  Sundays  ? 

You  may  tell  me  a  story  about  seven  ones. 

Write  on  the  board:    Seven  ones  are  seven. 

Seven  divided  by  Seven. 

How  many  yards  of  print,  at  seven  cents  a  yard,  can 
you  buy  for  seven  cents  ? 

How  many  pounds  of  potatoes,  at  seven  cents  a  pound, 
can  you  buy  for  seven  cents  ? 

How  many  bunches  of  violets,  at  seven  cents  a  bunch, 
can  you  buy  for  seven  cents? 


112  FIRST  STEPS   IN  NUMBER. 

How  many  roses,  at  seven  cents  a  rose,  can  you  buy  for 
seven  cents? 

How  many  loaves  of  bread,  at  seven  cents  a  loaf? 

How  many  bottles  of  ink,  at  seven  cents  a  bottle? 

How  many  quires  of  paper,  at  seven  cents  a  quire,  can 
be  bought  for  seven  cents  ? 

How  many  sponges,  at  seven  cents  a  sponge  ? 

Write :    There  is  one  seven  in  seven. 


§  22.   Comparison  of  Seven  with  Numbers  Known. 

If  you  have  seven  apples,  and  I  have  six  apples,  how 
many  more  have  you  than  I  ? 

If  a  horse  goes  seven  miles  an  hour,  and  a  mule  six  miles 
an  hour,  how  many  more  miles  does  the  horse  travel  than 
the  mule  ? 

There  are  seven  nuts  in  one  of  my  hands,  and  six  in  the 
other ;  how  many  more  in  one  than  in  the  other  ? 

If  you  have  seven  miles  to  ride,  and  I  have  six,  how 
much  farther  have  you  than  I  to  ride  ? 

If  Willie  has  seven  words  to  copy,  and  George  six,  how 
many  more  words  has  Willie  than  George  to  copy? 

John  has  seven  rabbits,  Cyrus  has  five ;  how  many  more 
rabbits  has  John  than  Cyrus  ? 

One  hen  has  seven  chickens,  another  hen  has  five  chick- 
ens ;  how  many  more  has  one  hen  than  the  other  ? 

I  can  pick  seven  quarts  of  berries  in  the  morning,  Mary 
can  pick  five ;  how  many  more  can  I  pick  than  Mary  ? 

There  are  seven  children  on  one  settee,  and  five  on 
another ;  how  many  more  are  there  on  one  than  on  the 
other  ? 

If  you  write  seven  stories  in  the  morning,  and  five  in 
the  afternoon,  how  many  more  do  you  write  in  the  morn- 
ing than  in  the  afternoon  ? 


THE   NUMBER  SEVEN.  113 

Seven  books  are  on  one  shelf  of  the  book-case,  and  four 
on  another;  how  many  more  are  on  one  than  on  the  other? 

There  are  seven  boys  and  four  girls  in  my  second  class ; 
how  many  more  boys  than  girls  are  there  ? 

How  many  more  strokes  does  the  clock  give  for  seven 
o'clock  than  for  four  o'clock  ? 

One  train  leaves  the  station  at  four  o'clock  in  the  after- 
noon, the  other  at  seven  o'clock  in  the  afternoon ;  how 
much  later  does  the  one  leave  than  the  other  ? 

If  half  a  pound  of  sago  costs  seven  cents,  and  half  a 
pound  of  rice  four  cents,  how  much  more  does  the  sago  cost 
than  the  rice  ? 

One  boy  earns  seven  cents  a  week,  another  boy  earns 
three  cents ;  how  much  more  does  one  earn  than  the 
other  ? 

It  costs  seven  cents  to  send  a  package  ;  how  much  more 
does  it  cost  than  to  send  an  ordinary  letter  ? 

There  were  seven  spools  of  thread  in  one  box,  and  three 
in  another ;  how  many  more  spools  were  there  in  one  than 
in  the  other  ? 

If  there  are  seven  plants  in  one  window,  and  three  in 
another,  how  many  more  are  there  in  one  than  in  the  other  ? 

If  there  are  seven  empty  chairs  in  one  row  of  seats,  and 
three  in  another  row,  how  many  more  empty  chairs  are 
there  in  one  row  than  in  the  other  ? 

There  are  seven  white  clouds  in  the  sky,  and  two  gray 
ones ;  how  many  more  white  clouds  are  there  than  gray 
ones? 

In  one  group  of  stars  there  are  seven  bright  stars,  in 
another  group  two  bright  stars ;  how  many  more  are  there 
in  one  than  in  the  other  ? 

If  I  wear  out  seven  pairs  of  shoes  in  a  year,  and  my 
brother  wears  out  but  two  pairs,  how  many  more  pairs  do 
I  wear  out  than  he  ? 


114  FIRST   STEPS   IN   NUMBER. 

Ellen  is  seven  years  old,  Eddie  is  two  years  old ;  how 
much  older  is  Ellen  than  Eddie  ? 

If  it  takes  seven  yards  of  cloth  to  make  me  a  dress,  and 
two  yards  to  make  little  Annie  a  dress,  how  much  more 
does  it  take  for  me  than  for  Annie  ? 

If  I  have  seven  letters  in  one  mail,  and  one  letter  in  an- 
other mail,  how  many  more  letters  do  I  get  in  one  mail 
than  in  the  other? 

There  are  seven  pencils  on  my  desk;  on  Ned's  desk  there 
is  one  pencil ;  how  many  more  pencils  are  there  on  my 
desk  than  on  Ned's  ? 

There  are  seven  blossoms  on  my  geranium,  but  only  one 
on  the  wax-plant ;  how  many  more  blossoms  are  there  on 
the  geranium  than  on  the  wax-plant  ? 

It  rained  each  day  last  week,  but  has  rained  only  one 
day  this  week ;  how  many  more  days  did  it  rain  last  week 
than  this  week  ? 

A  whistle  costs  one  cent,  a  toy  balloon  seven  cents ;  how 
much  more  does  the  balloon  cost  ? 


Show  me  that  seven 


is  one  more  than  six. 


Show  me  that  seven  is  two  more  than  five. 

Show  me  that  seven  is  three  more  than  four. 

Show  me  that  seven  is  four  more  than  three. 

Show  me  that  seven  is  five  more  than  two. 

Show  me  that  seven  is  six  more  than  one. 

If  I  have  one  cent,  how  much  more  must  I  earn  to  have 
seven  cents? 

If  Harry  has  two  doves,  how  many  more  must  he  get  to 
have  seven  doves? 

If  I  owe  you  seven  cents,  and  have  only  three  cents,  how 
many  more  cents  must  I  have  in  order  to  pay  you  ? 

On  this  stem  there  is  a  whorl  of  seven  leaves,  on  this 
stem  two  pairs  of  leaves ;  how  many  more  leaves  in  the 
whorl  than  in  the  two  pairs  ? 


THE   NUMBER  SEVEN.  115 

You  remain  in  school  five  hours  in  the  day  ;  how  many 
more  hours  would  you  remain  at  school  to  be  there  seven 
hours  ? 

I  have  six  yards  of  ribbon ;  I  wish  for  seven  yards ;  how 
many  more  yards  must  I  have  ? 

One  and  how  many  are  seven  ? 

Two  and  how  many  are  seven  ? 

Three  and  how  many  are  seven  ? 

Four  and  how  many  are  seven  ? 

Five  and  how  many  are  seven  ? 

Seven  and  how  many  are  seven  ? 

Seven  minus  what  number  equals  six  ? 

Seven  minus  what  number  equals  ^ve  ? 

Seven  minus  what  number  equals  four  ? 

Seven  minus  what  number  equals  three  ? 

Seven  minus  what  number  equals  two  ? 

Seven  minus  what  number  equals  one  ? 

Four  is  three  less  than  what  number  ? 

Three  is  four  less  than  what  number  ? 

Two  is  five  less  than  what  number? 

Five  is  two  less  than  what  number  ? 

One  is  six  less  than  what  number? 

Six  is  one  less  than  what  number  ? 

Show  me  a  row  of  seven  dots  on  the  board. 

Put  under  them  a  row  of  six  dots.  o  o  o  o  o  o  o 

Put  a  row  of  ^ve  dots.  ''o''o''o''o''o'' 

Make  a  row  of  four  dots.  o  o  o  o 

Make  three  dots  in  a  row.  o  o  o 

Make  two  dots.  o  o 

Make  one  dot.  ^ 

Tell  the  number  of  dots  as  I  point. 

(A  triangle  formed  by  making  seven  dots  in  a  row,  then 
six  below  them,  etc.,  gives  opportunity  to  compare  seven 
with  each  smaller  number,  in  different  ways.) 


116  FIRST  STEPS   IN   NUMBER. 

Show  me  a  number  that  is  one  less  than  seven ;  that  is 
two  less  than  seven.  Show  me  a  number  that  is  three  less 
than  seven ;  that  is  four  less  than  seven ;  that  is  six  less 
than  seven ;  that  is  five  less  than  seven  ;  that  is  no  less 
than  seven. 

For  seven  cents  how  many  one-cent  stamps  can  I  buy  ? 
How  many  two-cent  stamps,  and  how  many  cents  shall  I 
have  left?  How  many  three-cent  stamps,  and  what  will 
remain  ? 

How  many  four-cent  pencils  can  I  buy  for  seven  cents, 
and  how  many  cents  shall  I  have  left  ? 

How  many  oranges,  at  five  cents  an  orange,  can  be 
bought  for  seven  cents,  and  how  many  cents  will  be  left  ? 

How  many  dozen  buttons,  at  six  cents  a  dozen,  can  you 
buy  for  seven  cents,  and  how  much  money  will  you  have 
left? 

Exercise  for  Review. 

Name  four  days  of  the  week. 
Name  five  months. 
Name  six  holidays. 

Give  the  names  of  seven  children  you  know. 
Give  the  names  of  six  streets. 
Give  the  names  of  five  different  birds. 
Name  four  kinds  of  apples  you  have  eaten. 
What  three  strange  animals  did  you  see  at  the  menagerie? 
Name  seven  kinds  of  business  by  which  men  make  a 
living. 

Give  the  names  of  seven  different  kinds  of  trees. 

What  seven  different  flowers  have  you  seen  ? 

Name  seven  wild  flowers. 

Name  seven  cultivated  flowers. 

Tell  me  a  story  for  what  I  show  you. 

Tell  me  now  ;  and  now. 


THE  NUMBER  SEVEN.  117 

Read  wliat  I  show  you ;  again  ;  again  ;  and  again. 

Show  me  with  the  blocks  what  I  tell  you : 

If  I  have  seven  hens,  and  sell  five,  I  shall  have  two  hens. 

Mary  has  four  dolls  and  Annie  three  dolls ;  they  have 
together  seven  dolls. 

I  can  buy  three  apples,  at  two  cents  each,  with  seven 
cents,  and  have  one  cent  left. 

With  six  cents  I  can  buy  two  three-cent  stamps. 

If  a  six-quart  pail  is  half  full,  it  has  three  quarts  in  it. 

If  a  four-pint  pail  is  half  full,  it  has  two  pints  in  it. 

If  a  pint  of  hulled  corn  costs  three  cents,  a  quart  will  cost 
six  cents. 

If  one  peach  costs  one  cent,  six  peaches  will  cost  six  cents. 

In  three  quarts  there  are  six  pints. 

In  one  pint  there  are  four  gills. 

If  I  owe  you  seven  cents,  and  pay  you  in  three  pieces  of 
money,  I  can  give  you  a  three-cent  coin  and  two  two-cent 
coins ;  or,  I  can  give  you  a  five-cent  coin  and  two  cents ; 
or,  I  can  give  you  two  three-cent  coins  and  one  cent. 

You  may  find  what  the  pieces  of  money  will  be  if  I  pay 
you  seven  cents  with  five  pieces  of  money  ;  if  I  pay  you 
with  six  pieces  of  money ;  if  I  pay  you  with  two  pieces  of 
money. 

Draw  a  line  an  inch  long  for  every  day  in  the  week  but 
Saturday ;  draw  a  line  two  inches  long  for  Saturday. 
Measure  to  see  if  you  drew  each  line  the  right  length. 

You  may  guess  how  long  this  envelope  is ;  how  wide  it 
is.  How  long  this  book  is ;  how  wide  it  is.  How  long  a 
side  of  this  square  is.  How  long  a  side  of  this  triangle  is. 
How  thick  this  book  is.  How  deep  this  box  is.  How  high 
this  spool  is. 

What  two  equal  numbers  make  four  ? 

What  two  equal  numbers  make  six  ? 

What  two  equal  numbers  make  two  ? 


118  FIRST  STEPS   IN   NUMBER. 

What  two  equal  numbers  and  one  make  five  ? 
What  three  equal  numbers  make  six  ? 
What  three  equal  numbers  make  three  ? 
What  three  equal  numbers  and  one  make  seven  ? 
See  these  stories  I  have  written  on  the  board: 

Three  and  one  are  — .  Two  and  three  are  — . 

Four  and  two  are  — .  Five  and  two  are  — . 

Four  and  three  are  — .  Three  and  four  are  — . 

Three  twos  are  — .  Two  twos  are  — . 

Six  minus  four  are  — .  Five  minus  three  are  — . 

Seven  minus  five  are  — .  Seven  minus  two  are  — . 

Seven  minus  four  are  — .         Seven  minus  three  are  — . 
There  are  two  threes  in  — .     There  are  three  twos  in  — . 

There  are  two  twos  and  one  in  — . 

There  are  three  twos  and  one  in  — , 

Who  knows  what  word  to  put  in  place  of  the  blank  in 
the  first  story  ?  in  the  second  story  ?  in  the  other  stories  ? 

(Let  the  blank  in  each  case  be  filled  with  the  proper 
word  ;  the  child  writing  the  word.) 

Illustrate  what  I  tell  you : 

Of  seven  pocket  knives  which  I  saw,  three  only  had 
blades  open ;  how  many  had  the  blades  shut  ? 

Of  seven  apples  which  were  on  the  table,  five  had  no 
stem  ;  how  many  had  stems  ? 

Five  tops  were  spinning,  but  two  have  fallen  over ;  how 
many  tops  are  spinning? 

Four  cups  are  right  side  up  on  the  table,  and  three  are 
up  side  down ;  how  many  cups  are  on  the  table  ? 

Four  pears  and  two  pears  are  how  many  pears? 


CHAPTER  VII. 

THE    NUMBER    EIGHT. 


§23.   Eight  as  a  Whole. 

Take  seven  blocks.  Take  one  more  block.  Do  you 
know  how  many  blocks  you  have  ?     You  have  eight  blocks. 

Show  me  eight  chestnuts ;  eight  spools ;  eight  beans ; 
eight  buttons  ;  eight  fingers ;  eight  books ;  eight  pencils ; 
eight  marks  on  the  blackboard ;  eight  rounds  on  the  settee ; 
eight  chair-legs ;  eight  desk-stands ;  eight  children  at  work ; 
eight  words  on  the  blackboard. 

Name  eight  things  that  you  have  seen  at  home ;  on  the 
street. 

Tell  me  eight  things  you  have  seen  at  the  fair. 

Tell  me  eight  things  you  can  do. 

Arrange  eight  dots  on  the  board  in  all  the  different  ways 
you  can. 

Name  eight  letters  you  have  learned  to  write. 

Name  eight  words  you  can  write,  and  take  a  block  for 
each  word. 

Name  eight  numbers  you  know. 

Name  eight  vegetables ;  eight  animals  ;  eight  pieces  of 
furniture ;  eight  sounds  you  hear  every  day  ;  eight  differ- 
ent things  you  can  see  in  the  room. 

Copy  the  word  eight  on  your  slate. 

Take  eight  splints  and  arrange  them  all  the  ways  you 
can.     Copy  the  figures  which  you  make  with  the  splints. 


120  FIRST  STEPS   IN   NUMBER. 

§24.   Discoveries  in  Eight. 

Who  can  find  two  numbers  that  together  make  eight? 

What  two  numbers  make  eight  ? 

Name  every  two  numbers  which  together  make  eight. 

What  numbers  can  you  find  in  eight? 

What  will  remain  after  taking  each  one  of  these  numbers 
from  eight  ? 

What  two  equal  numbers  make  eight  ? 

What  four  equal  numbers  make  eight? 

What  eight  equal  numbers  make  eight? 

What  one  number  makes  eight? 

How  many  fours  can  you  find  in  eight?  How  many 
twos  ?     How  many  ones  ?     How  many  eights  ? 

Show  me  one  half  of  eight ;  two  halves  of  eight. 

What  is  one  half  of  eight  ?  two  halves  of  eight  ? 

§25.   Facts  in  Eight. 
Seven  and  One. 

Each  take  seven  blocks.  Take  one  more  block.  How 
many  blocks  are  seven  blocks  and  one  block  ? 

Show  me  eight  other  objects  in  seven  and  one. 

I  can  see  on  my  chart  seven  stars,  and  one  more  star  in 
the  same  row.  Who  sees  what  I  see  ?  How  many  stars 
do  you  see  ? 

Tell  me  a  story  about  this. 

Tell  me  a  story  about  seven  cows  and  one  cow. 

Tell  me  a  story  about  seven  daisies  and  one  daisy. 

Tell  me  a  story  about  seven  butterflies  and  one  butterfly. 

Tell  me  a  story  about  seven  eagles  and  one  eagle. 

Tell  me  a  story  about  seven  buttercups  and  one  buttercup. 

If  the  week  had  one  more  day,  how  many  days  would 
there  be  in  a  week  ? 


THE   NUMBER   EIGHT.  121 

It  took  a  week  and  one  more  day  to  cross  the  Atlantic 
Ocean ;  how  many  days  did  it  take  ? 

In  two  months  there  are  seven  weeks  and  one  week ; 
how  many  weeks  in  two  months  ? 

George  is  seven  years  old  ;  how  old  will  he  be  a  year 
from  now  ? 

I  have  learned  seven  stanzas  of  a  hymn,  and  there  is  one 
more  stanza  to  learn  ;  how  many  stanzas  has  the  hymn  ? 

There  were  seven  wheels  on  a  car,  and  one  more  wheel 
was  ready  to  be  put  on  ;  how  many  wheels  would  there  be 
on  the  car  when  this  one  was  put  on  ? 

Tell  me  stories  about  seven  and  one. 

Write :  Seven  and  one  are  eight. 

One  and  Seven.  ^ 

Show  me  one  block.     Show  me  seven  more. 

One  block  and  seven  blocks  are  how  many  blocks  ? 

One  spool  and  seven  spools  are  how  many  spools  ? 

One  horse  and  seven  horses  are  how  many  horses? 

One  man  and  seven  men  are  how  many  men  ? 

Tell  me  a  story  about  one  and  seven ;  another ;  another; 
another ;  another. 

In  one  corner  of  this  card  there  is  one  dot,  and  in  another 
corner  seven  dots ;  how  many  dots  are  there  on  the  card  ? 

If  I  have  one  stick  of  randy,  and  Jennie  has  seven,  how 
many  have  both  of  us  ? 

I  paid  one  cent  for  a  skein  of  linen  thread,  and  seven 
cents  for  a  spool  of  linen  thread ;  how  much  did  both  cost? 

I  have  one  rooster  and  seven  hens ;  how  many  fowls  have 
I  in  all? 

On  Susie's  eighth  birthday  she  had  a  party,  to  which  she 
invited  seven  children.  How  many  children  were  there  in 
all? 

Write  :  One  and  seven  are  eight. 


122  FIRST   STEPS   IN   NUMBER. 


Eight  minus  One. 

Show  me  eight  blocks. 

Do  as  I  do.     (Teacher  puts  one  under  the  table.) 

How  many  have  you  left  ? 

How  many  did  you  take  away  ? 

Tell  me  about  eight  blocks  minus  one  block. 

Call  your  blocks  rabbits,  and  tell  me  the  same  story. 

Call  them  pigeons ;  call  them  chickens ;  call  them  geese 
'swimming  in  the  pond ;  call  them  ducks ;  call  them  snails ; 
lall  them  grasshoppers. 

If  there  were  eight  wheels  on  a  car,  and  one  fell  off,  how 
many  would  be  left  on  the  car  ? 

^     If  there  are  eight  persons  in  a  car,  and  one  gets  out,  how 
many  remain  in  the  car? 

Write  :    Eight  minus  one  are  seven. 


Eight  minus  Seven. 

Take  eight  blocks ;  put  back  seven ;  how  many  have 
you  left? 

Take  eight  buttons  ;  put  back  seven  ;  how  many  have 
you  left? 

Make  eight  dots  on  the  board ;  draw  a  line  through 
seven  ;  how  many  are  left  ? 

Draw  eight  straight  lines  on  the  board ;  erase  seven ;  how 
many  are  left? 

If  there  are  eight  ink-wells  to  fill,  and  I  fill  seven,  how 
many  remain  to  be  filled  ? 

If  eight  boys  are  on  a  sled,  and  seven  fall  off,  how  many 
boys  are  left  on  the  sled  ? 

Eight  sheep  are  in  a  pasture.  If  seven  get  out,  how 
many  will  be  left  in  the  pasture  ? 


THE   NUMBER   EIGHT.  123 

Eight  potatoes  grew  in  a  liill ;  seven  were  nice  and  large, 
tlie  rest  were  small ;  how  many  were  small  ? 

Eight  turkeys  roosted  in  an  open  field  ;  seven  on  the 
fence,  and  the  rest  on  the  bars ;  how  many  roosted  on  the 
bars? 

Tell  me  a  story  about  eight  minus  seven. 

"Write  on  your  slate :    Eight  minus  seven  is  one. 

One-Fourth. 

You  may  cut  this  apple  into  halves.  Cut  each  half  into 
halves.     Into  how  many  pieces  have  you  cut  the  apple  ? 

Cut  this  paper  ring  into  halves.  Cut  each  half  into 
halves.      Into  how  many  parts  have  you  divided  the  ring  ? 

Divide  this  circle  in  the  same  way.  Into  how  many 
pieces  have  you  cut  the  circle  ? 

Divide  this  star  in  the  same  way.  Into  how  many 
pieces  have  you  cut  the  star  ? 

Divide  this  square  I  have  on  the  board  into  halves,  by 
drawing  a  line  from  top  to  bottom.  Divide  each  half  into 
halves,  by  drawing  a  line  from  left  to  right.  Into  how 
many  parts  is  the  square  divided? 

Divide  this  square  into  halyes,  by  drawing  a  line  from 
corner  to  corner.  Connect  the  other  two  corners.  Into 
how  many  parts  have  you  divided  the  square  ?  Look  at 
the  parts,  and  tell  me  which  is  the  largest  part.  Into  what 
kind  of  parts,  then,  have  you  divided  the  square? 

Into  what  kind  of  parts  did  you  divide  the  first  square  ? 
Into  how  many  equal  parts  ? 

Into  what  kind  of  parts  is  the  star  divided,  and  how 
many  parts  ? 

How  have  you  divided  the  circle  ? 

How  have  you  divided  the  paper  ring  ? 

How  have  you  divided  the  apple  ? 


124  FIRST  STEPS   IN   NUMBER. 

Show  me  one  of  the  four  equal  parts  into  which  the  apple 
is  divided.  It  is  a  fourth  of  the  apple.  Show  me  another 
of  the  four  equal  parts  into  which  the  apple  is  divided.  It 
is  a  fourth  of  the  apple.  Show  me  another  fourth  of  the 
apple  ;  another  fourth.  Show  me  one  of  the  four  equal 
parts  of  the  ring.  What  part  of  the  ring  is  it  ?  Show  me 
each  fourth  of  the  ring.  Each  fourth  of  the  star.  Make  a 
cross  in  one  fourth  of  the  square  that  is  divided  into  trian- 
gles. Make  a  dot  in  another  fourth.  Make  a  straight  line 
in  another  fourth.  Make  the  letter  i  in  the  last  fourth. 
Look  at  the  square  that  is  divided  into  squares.  What 
part  of  the  large  square  is  each  small  square  ? 

Divide  this  triangle  into  fourths,  by  drawing  lines  from 
the  top  to  the  base. 

Divide  this  string  into  fourths. 

Divide  this  sheet  of  paper  into  fourths. 

Divide  this  strip  of  paper  into  fourths. 
.  Divide  this  stick  into  fourths. 

Mark  off  this  line  into  fourths. 

What  have  you  seen  cut  into  fourths  ? 

Into  how  many  pieces  was  it  cut  ?  Into  what  kind  of 
pieces  ? 

If  I  cut  a  pie  into  four  equal  pieces,  what  part  of  the 
whole  pie  is  one  piece?  What  part  of  the  pie  are  two 
pieces  ?  Four  pieces  will  make  what  part  of  the  pie  ? 
What  part  are  three  pieces  ? 

If  an  orange  is  cut  into  four  equal  pieces,  what  part  of 
the  orange  is  each  piece  ?  What  part  of  the  orange  are  two 
pieces  ?  are  three  pieces  ?  are  four  pieces  ? 

If  a  peach  is  divided  into  four  equal  pieces,  what  part  of 
the  peach  is  one  piece?  are  two  pieces?  are  three  pieces? 
are  four  pieces  ? 

If  a  pear  is  divided  into  four  equal  pieces,  what  part  of 
the  pear  is  each  piece  ?  are  three  pieces  ?  are  four  pieces  ? 


THE  NUMBER   EIGHT.  125 

If  you  divide  an  apple  into  fourths,  into  how  many  parts 
do  you  divide  it  ?  Into  what  kind  of  parts  ?  If  you  divide 
a  stick  into  fourths,  into  how  many  parts  do  you  divide  it? 
Into  what  kind  of  parts  ?  If  you  divide  four  blocks  into 
fourths,  into  how  many  groups  do  you  divide  them  ?  How 
many  blocks  are  there  in  each  group  ?  Show  me  one  fourth 
of  four ;  two  fourths  of  four ;  three  fourths  of  four ;  four 
fourths  of  four.  Divide  eight  blocks  into  fourths.  Into 
how  many  groups  have  you  divided  them  ?  Into  what  kind 
of  groups  ?  Show  me  one  fourth  of  eight ;  two  fourths  of 
eight ;  three  fourths  of  eight ;  four  fourths  of  eight.  What 
is  one  fourth  of  eight?  What  is  one  fourth  of  four  ?  What 
are  three  fourths  of  four?  two  fourths  of  four?  What  is  half 
of  four? 

Six  and  Two. 

You  may  each  take  six  blocks ;  take  two  more ;  how 
many  blocks  have  you  ?  Six  blocks  and  two  blocks  are 
how  many  blocks? 

Show  me  six  straight  lines  on  the  board ;  show  me  two 
more  straight  lines;  how  many  straight  lines  are  there  in  all? 

Show  me  six  paper  patterns ;  show  me  two  more ;  how 
many  are  there  in  all  ? 

Tell  me  a  story  for  six  and  two  ;  another ;  another. 

I  have  six  children  on  this  side  of  the  table,  and  two 
more  on  this  side  of  the  table.  How  many,  children  are 
about  the  table  ? 

If  George  writes  the  word  cup  six  times,  and  then  writes 
it  two  more  times,  how  many  times  does  he  write  it  in  all  ? 

If  there  are  six  men  on  the  car-platform,  and  two  more 
jump  on,  how  many  are  there  on  the  platform? 

Jamie  found  six  eggs  in  one  nest,  and  two  in  another ; 
how  many  eggs  did  he  find  in  both  nests? 

Write  :  Six  and  two  are  eight. 


126  FIRST  STEPS   IN   NUMBEK. 

Two  and  Six. 

Make  two  dots  on  the  board  ;  make  six  more  dots  ;  how 
many  dots  have  you  made  ? 

Draw  two  lines  ;  draw  six  more  lines ;  how  many  lines 
have  you  drawn  ? 

Find  two  paper  knives  ;  find  six  more  ;  how  many  paper 
knives  have  you  found  ? 

If  I  get  two  letters  in  the  moining  mail,  and  six  in  the 
evening,  how  many  letters  do  I  receive  ? 

If  I  have  covered  two  books,  and  have  six  more  to  cover, 
how  many  books  had  I  to  cover  at  first  ? 

One  cat  has  two  kittens ;  another  has  six  kittens ;  how 
many  kittens  have  both  cats  ? 

I  have  two  pencils  nicely  sharpened,  and  six  more  to 
sharpen  ;  how  many  pencils  have  I  ? 

A  post  is  two  feet  in  the  ground,  and  six  feet  out  of  the 
ground ;  how  many  feet  are  there  in  the  post  ? 

Write :  Two  and  six  are  eight. 

Eight  minus  T^vo. 

A  man  had  eight  cows,  but  sold  two  ;  how  many  did  he 
then  have  ? 

There  were  eight  trees  in  a  row,  but  two  died  ;  how  many 
lived  ? 

The  price  of  a  book  was  eight  cents,  but  the  bookseller 
took  oflT  two  cents  because  the  cover  was  marred ;  how 
much  was  paid  for  the  book  ? 

A  little  girl  braids  eight  yards  of  matting  each  day  ; 
when  she  has  braided  two  yards,  how  many  more  yards  has 
she  to  braid  ? 

John  caught  eight  fish,  but  put  two  back  in  the  water ; 
how  many  did  he  have  to  carry  home  ? 


THE  NUMBER  EIGHT.  127 

We  have  eight  quarts  of  milk  a  day;  if  we  use  two 
quarts  at  breakfast,  how  many  quarts  are  left  ? 

Ellen  picked  eight  quarts  of  blueberries,  but  spilled  two 
quarts ;  how  many  quarts  did  she  then  have  ? 

Addie  can  work  eight  inches  of  lace  in  a  day ;  when  she 
has  worked  two  inches,  how  many  more  inches  can  she 
work  during  the  day  ? 

Write :    Eight  minus  two  are  six. 

Eight  minus  Six. 

Eight  little  girls  are  weaving  paper  mats ;  six  mats  will 
be  finished  to-day ;  how  many  will  be  left  unfinished  ? 

Eddie  wrote  eight  words  on  his  slate ;  six  were  right ; 
how  many  were  wrong  ? 

I  have  eight  calls  to  make ;  after  I  have  made  six  calls, 
how  many  more  calls  have  I  to  make  ? 

Eight  children  were  playing  store ;  six  thought  they 
would  set  up  a  store  by  themselves  ;  how  many  were  left 
to  run  the  first  store  ? 

Eight  girls  were  playing  "Drop  the  handkerchief";  six 
were  clapped  out  of  the  ring ;  how  many  were  left  ? 

Eight  boys  were  playing  "Fox  and  geese";  six  were 
geese ;  how  many  were  foxes  ? 

Eight  boys  were  playing  ball ;  six  took  turns  in  throwing 
the  ball,  and  the  rest  batted  the  ball ;  how  many  batted 
the  ball? 

Willie  is  going  to  have  eight  turrets  to  his  block-castle  ; 
he  has  built  six ;  how  many  more  has  he  to  build  ? 

I  have  a  five-cent  piece,  a  two-cent  piece,  and  one  cent. 
If  I  spend  six  cents,  how  many  cents  shall  I  have  left  ? 

Tell  me  stories  about  eight  minus  six. 

Write  :   Eight  minus  six  are  two. 


128  FIRST  STEPS   IN   NUMBER. 

Eight  divided  by  Two. 

Take  eight  blocks.  Put  your  eight  blocks  into  groups 
of  two.     How  many  two-blocks  in  eight  blocks  ? 

Find  how  many  two-dots  there  are  in  eight  dots. 

Here  are  eight  paper  shoes ;  put  them  in  pairs  ;  how 
many  pairs  of  shoes  do  you  find  in  the  eight  shoes  ? 

Here  are  eight  skates  ;  put  them  in  pairs ;  how  many 
pairs  of  skates  do  you  find  in  eight  skates  ? 

Put  these  eight  horses  into  spans  of  horses  ;  how  many 
spans  of  horses  do  you 'find  in  eight  horses? 

Put^hese  mittens  into  pairs  ;  how  many  pairs  of  mittens 
in  eight  mittens  ? 

How  many  couples  of  buttons  in  eight  buttons  ? 

How  many  yokes  of  oxen  in  eight  oxen  ? 

How  many  pairs  of  ear-rings  in  eight  ear-rings  ? 

How  many  pairs  of  bracelets  in  eight  bracelets  ? 

How  many  brace  of  ducks  in  eight  ducks  ? 

A  carriage-maker  puts  two  wheels  on  each  baby-carriage ; 
how  many  carriages  will  eight  wheels  supply  ? 

A  family  uses  two  pounds  of  butter  a  day ;  how  many 
days  will  eight  pounds  last  the  family  ? 

In  eight  pints  how  many  quarts  ? 

It  requires  two  knobs  for  each  drawer;  on  how  many 
drawers  will  a  cabinet-maker  put  eight  knobs  ? 

On  how  many  trunks  will  a  trunk-maker  put  eight 
handles  ? 

If  there  are  two  pedals  to  each  piano,  eight  pedals  will 
supply  how  many  pianos  ? 

Eight  cents  will  buy  how  many  two-cent  postage-stamps? 

If  I  owe  you  eight  cents,  and  pay  you  in  two-cent  coins, 
how  many  must  I  give  you  ? 

Tell  me  a  story  about  eight  divided  by  two. 

Write :    There  are  four  twos  in  eight. 


THE   NUMBER   EIGHT.  129 


Four  Twos. 


Make  two  dots  on  the  board ;  make  below  them  two  more 
dots ;  below  these  two  other  dots ;  and  under  all  another 
two  dots.  How  many  two-dots  have  you  made  ?  how  many 
dots? 

Make  lines  on  the  board  in  the  same  way.  How  many 
two-lines  have  you  drawn  ?  how  many  lines  ? 

Show  me  four  two-blocks;  how  many  blocks  do  you 
show  me  ? 

Show  me  four  two-pitchers ;  how  many  pitchers  have  you 
shown  me  ? 

Show  me  four  kinds  of  blocks,  and  two  of  a  kind ;  how 
many  blocks  have  you  shown  me  ? 

Show  me  four  kinds  of  buttons,  two  of  a  kind;  how 
many  buttons  do  you  show  me? 

How  many  hands  have  four  boys  ? 

How  many  feet  have  four  boys  ? 

How  many  wings  have  four  birds  V 

How  many  legs  have  four  chickens  ? 

How  many  rockers  have  four  rocking-chairs? 

How  many  leaves  have  four  sheets  of  paper  ? 

How  many  handles  have  four  pairs  of  scissors? 

How  many  legs  have  four  pairs  of  compasses  ? 

How  many  blades  have  four  pairs  of  scissors  ? 

How  many  cents  will  four  two-cent  books  cost  ? 

How  many  cents  will  four  two-cent  sticks  of  taffy  cost  ? 

Think  of  what  you  can  buy  for  two  cents,  and  tell  me 
what  four  will  cost. 

Illustrate  on  the  board  the  examples  I  give  you,  and  tell 
me  the  answers  :  — 

Ned  has  two  doves ;    George  has  four  times  as  many. 

If  there  are  two  eggs  in  one  nest,  how  many  are  there  in 
four  nests? 


130 


FIRST  STEPS   IN   NUMBER. 


On  a  baby-carriage  there  are  two  wheels ;  on  a  car  there 
are  four  times  as  many  wheels. 

Nellie  has  two  dolls ;  Annie  has  four  times  as  many  dolls. 
There  are  two  plants  in  each  of  four  windows. 
Four  knives  have  each  two  blades. 
Four  desks  have  each  two  stands. 
Write :   Four  twos  are  eight. 


Exercise  for  Review. 

Name  the  number  of  dots  as  I  point. 


•  • 
• 

• 
• 

•  • 

•• 

• 

•  • 

•       • 

•     •     • 

•  ••• 

•  •  •  • 

•  • 

•  • 

• 

•    • 

•    •    • 

•  «  • 

•  •  • 


Eead  as  I  erase  dots. 
Tell  me  a  story  for  what  I 
"Write  the  right  word  in 
Btories :  — 

Four  and  —  are  six. 
Five  and  two  are  — . 
Two  and  six  are  — . 
Four  and  —  are  seven. 
Three  and  four  are  — . 
Seven  minus  —  are  five. 
Seven  minus  —  are  three. 
Eight  minus  six  are  — . 
Two  and  —  are  four. 


show  you  with  the  dots, 
place  of  the  blank,  in  thes9 

Four  and  two  are  — . 
Six  and  two  are  — . 
Five  and  —  are  seven. 
Four  and  three  are  — . 
Three  and  —  are  seven. 
Seven  minus  two  are  — . 
Seven  minus  four  are  — . 
Eight  minus  two  are  — . 
Two  twos  are  — . 


THE   NUMBER   EIGHT.  131 

Three  and  —  are  six.  Three  twos  are  — . 

Two  threes  are  — .  Two  —  are  six. 

There  are  two  threes  in  — .     Four  twos  are  — . 

There  are  four  twos  in  — .       There  are  three  twos  in  — . 
Divide  this  square  into  halves. 
Divide  it  into  fourths. 
Divide  this  triangle  into  halves. 
Divide  it  into  fourths. 

To  divide  this  apple  into  halves,  into  how  many  pieces 
must  I  cut  it  ?  into  what  kind  of  pieces  ?  and  what  part  of 
the  apple  is  each  piece  ? 

Show  me  one  half  of  two ;  one  half  of  four ;  one  half  of 
six  ;  one  half  of  eight. 

I  have  cut  this  apple  into  halves ;  you  may  finish  cutting 
it,  so  that  it  will  be  in  fourths.  In  how  many  pieces  is  the 
apple  divided?  in  what  kind  of  pieces?  and  what  part  of 
the  apple  is  each  piece  ? 

Mark  oiF  your  slate  into  fourths. 

Fold  this  handkerchief  into  fourths. 

Mark  off  the  Board  into  fourths. 

Show  me  what  you  think  to  be  a  fourth  of  your  pencil ; 
of  your  finger  ;  of  this  table  ;  of  this  line  ;  of  this  book. 

Show  me  one  fourth  of  four  blocks ;  one  fourth  of  four 
crayons  ;  one  fourth  of  four  pencils. 

Divide  eight  blocks  into  fourths.  Show  me  one  fourth  of 
eight  blocks ;  two  fourths  of  eight  blocks ;  three  fourths  of 
eight  blocks ;  four  fourths  of  eight. 

How  many  gills  of  water  in  a  pint  of  water  ? 

How  many  gills  in  one  fourth  of  a  pint  of  water?  in  two 
fourths  of  a  pint  ?  in  half  a  pint  ? 

If  one  gill  of  water  weighs  two  ounces,  what  will  a  pint 
of  water  weigh  ? 

If  one  gill  of  peanuts  costs  two  cents,  what  will  a  pint  of 
peanuts  cost? 


132  FII^ST  STEPS   IN   NUMBER. 

If  one  gill  of  milk  will  half  fill  a  cup,  how  many  gills 
will  the  cup  hold  ?  What  part  of  a  pint  will  the  cup  hold? 
How  many  cupfuls  will  make  a  pint  ? 

My  watch  loses  six  seconds  a  day,  and  my  brother's  gains 
two  seconds  a  day ;  if  the  watches  are  together  in  the 
morning,  how  much  difference  is  there  the  next  morning  ? 

It  is  six  miles  to  Boston ;  how  many  miles  is  it  half-way 
to  Boston  ? 

If  I  walk  two  miles,  and  ride  six  miles,  how  many  miles 
do  I  travel  ? 

If  I  have  eight  cents,  and  buy  a  top  for  two  cents,  and  a 
thimble  for  six  cents,  how  many  cents  have  I  left  ? 

If  a  boy  earns  two  cents  a  day  for  Tuesday  and  Friday, 
and  one  cent  for  each  of  the  other  days  in  the  week,  how 
many  cents  will  he  earn  during  the  week  ? 

Alice  bought  a  pencil  for  one  cent,  a  book  for  one  cent, 
six  sheets  of  paper  for  one  cent,  a  rubber  for  two  cents,  and 
a  sponge  for  two  cents,  and  had  one  cent  left ;  how  many 
cents  did  she  have  at  first? 

My  wax-plant  had  two  blossoms  the  first  year,  twice  as 
many  the  second  year,  and  the  third  year  as  many  as  it 
had  the  first  and  second  years  together ;  how  many  blos- 
soms did  it  have  the  third  year  ? 

How  many  shells  have  four  oysters?  four  clams?  four 
snails  ? 

If  you  divide  an  apple  so  as  to  give  me  three  times  as 
much  as  you  have,  how  will  you  divide  the  apple  ?  What 
part  of  the  apple  will  you  have  ?  What  part  of  the  apple 
shall  I  have? 

If  you  divide  a  pie  into  tw^o  pieces,  so  that  one  piece  will 
be  three  times  as  large  as  the  other,  what  part  of  the  pie 
will  each  piece  be  ? 

If  you  divide  an  orange  equally  among  four  persons,  what 
part  of  the  orange  do  you  give  each  person  ? 


THE   NUMBER  EIGHT.  133 

If  you  pour  .a  pint  of  milk  into  four  cups,  each  of  the 
same  size,  how  much  will  each  cup  hold  ?  What  part  of  a 
pint  will  each  cup  hold  ? 

If  you  pour  a  quart  of  berries  into  four  cups,  each  of  the 
same  size,  how  much  will  each  cup  hold  ?  What  part  of  a 
quart  will  each  cup  hold  ? 

This  line  is  four  inches  long.  Show  me  what  you  think 
to  be  a  fourth  of  the  line.  How  long  is  a  fourth  of  the 
line? 

This  line  is  eight  inches  long.  Show  me  what  you  think 
to  be  a  fourth  of  the  line.    How  long  is  a  fourth  of  the  line? 

Divide  a  square  into  four  equal  parts,  by  drawing  a  line 
from  top  to  bottom,  and  a  line  from  left  to  right ;  connect 
the  corners,  and  tell  me  into  how  many  parts  you  have 
divided  the  square. 

We  own  a  horse,  two  cows,  a  sheep,  a  dog,  and  two  cats. 
How  many  animals  do  we  own  ? 

Ed  has  two  white  hens,  two  gray  hens,  two  black  hens, 
and  enough  speckled  hens  to  make  eight  hens ;  how^  many 
speckled  hens  has  he  ?    • 

If  two  quarts  of  skim-milk  cost  me  nothing,  what  will 
eight  quarts  of  skim-milk  cost  me  at  the  same  rate  ? 

If  I  have  four  cents,  how  many  whistles  at  eight  cents  a 
whistle  can  I  buy  ? 

If  I  have  six  cents,  how  many  whistles  at  eight  cents  a 
whistle  can  I  buy  ?  How  many  more  cents  must  I  have  to 
buy  one  whistle? 

One  block,  and  three  blocks,  and  three  blocks,  minus 
seven  blocks,  are  how  many  blocks  ? 

In  looking  over  my  gloves  I  found  eight  gloves  ;  one  was 
an  odd  glove  ;  how  many  others  were  odd  ?  How  many 
pairs  of  gloves  had  I  ? 

There  are  four  hacks  front  of  the  station ;  each  has  two 
horses ;  how  many  horses  are  there  front  of  the  station  ? 


134  VmS'X  STEPS  IN  KUMBER. 

Two  persons  can  ride  in  a  herdic  ;  how  many  persons 
will  four  herdics  carry  ? 

Jack  blacked  eight  boots  before  breakfast ;  how  many 
pairs  of  boots  did  he  black  ? 

A  fish  has  three  fins  on  each  side ;  how  many  fins  has 
the  fish? 

Each  fish  has  two  gills;  how  many  gills  have  three 
fishes  ? 

One  milking-stool  has  three  legs ;  how  many  legs  have 
two  milking-stools  ? 

In  a  dish  are  six  apples ;  how  many  of  us  can  take  out 
two  ?  how  many  of  us  can  take  three  ? 

Count  by  twos  to  eight. 

Count  backward  from  eight  by  twos. 

Five  and  Three. 

Show  me  five  fingers  ;  show  me  three  fingers ;  how  many 
fingers  do  you  show  me  ? 

See  if  five  dots  and  three  dots  are  eight  dots. 

Here  is  a  picture  of  five  chickens  on  the  ground  and 
three  in  the  cherry-tree  ;  how  many  chickens  can  you  see  ? 

Here  are  five  rabbits  eating  clover,  and  three  eating  cab- 
bage ;  how  many  rabbits  can  you  see  ? 

Harry  has  five  doves  and  three  kittens ;  how  many  pets 
has  he  ? 

If  I  give  you  a  five-cent  coin  and  a  three-cent  coin,  how 
many  cents  do  I  give  you  ? 

How  many  cents  must  you  pay  for  a  five-cent  stamp 
and  a  three-cent  stamp  ? 

What  must  I  pay  for  a  five-cent  ticket  and  a  three-cent 
ticket? 

Tell  me  stories  about  five  and  three. 

Write  :    Five  and  three  are  eight. 


THE  nxjMBER  eight.  135 


Three  and  Five. 

There  are  three  children  on  the  settee ;  five  more  may 
sit  with  them  ;  how  many  children  are  now  on  the  settee  ? 

Here  is  a  card  with  three  dots  in  one  half  and  five  in 
the  other  half ;  how  many  dots  are  on  the  card  ? 

Here  are  three  spools,  which  we  will  call  soldiers ;  five 
more  soldiers  march  up  to  them ;  how  many  soldiers  are 
now  standing  here  ? 

Three  geese  set  up  a  cackle,  and  five  more  joined  in ; 
how  many  geese  were  then  cackling  ? 

One  bracket  has  three  cups,  and  another  has  five  cups ; 
how  many  plants  will  the  two  brackets  hold  ? 

If  a  farmer  sleeps  three  hours  before  midnight,  and  five 
hours  after  midnight,  how  many  hours  does  he  sleep  ? 

Tell  me  stories  about  three  and  five. 

Write  :    Three  and  five  are  eight. 


Eight  minus  Three. 

Show  me  eight  fingers ;  shut  three  fingers ;  how  many 
fingers  are  open  ? 

Show  me  eight  blocks ;  put  three  under  the  table ;  how 
many  blocks  have  you  left  ? 

Find  eight  stars ;  put  three  stars  behind  you  ;  how  many 
stars  have  you  on  the  table? 

Find  eight  birds ;  let  three  fly  away ;  how  many  have 
you  left? 

Call  these  buttons  eight  frogs;  three  have  now  jumped 
into  the  pond  ;  how  many  frogs  remain  ? 

Mary  knit  eight  inches  of  edging,  but  the  kitten  got  hold 
of  the  spool  of  thread  and  ravelled  out  three  inches ;  how 
many  inches  of  edging  had  she  then  ? 


136  FIRST  STEPS   IN   NUMBER. 

In  a  chandelier  of  eight  lamps,  three  were  lighted ;  how 
many  were  not  lighted  ? 

There  were  eight  tassels  on  my  scrap-bag,  but  three  have 
fallen  off;  how  many  are  now  on  the^crap-bag ? 

Tell  me  stories  about  eight  minus  three. 

Write:    Eight  minus  three  are  five. 

Eight  minus  Five. 

Draw  eight  lines  on  the  board,  and  cross  five  lines ;  how 
many  lines  are  not  crossed  ? 

Make  eight  dots  straight  up  and  down  on  the  board ; 
draw  a  line  through  five ;  how  many  have  no  line  drawn 
through  them  ? 

Make  eight  dots  in  a  slanting  line,  and  erase  five ;  how 
many  remain  ? 

Make  eight  crosses  on  the  board ;  cover  up  five ;  how^ 
many  can  you  see  ? 

Write  eight  is ;  join  five  of  them ;  how  many  are  not 
joined  ? 

I  had  eight  pencils  to  sharpen  ;  I  have  sharpened  five  ; 
how  many  remain  to  be  sharpened  ? 

I  have  eight  fans  to  paint ;  after  I  have  painted  five,  how 
many  will  remain  to  be  painted  ? 

There  are  eight  weeks  in  two  months ;  if  I  have  two 
months'  vacation,  and  am  busy  five  weeks,  how  many  weeks 
have  I  to  rest  ? 

If  I  have  two  pints  of  milk,  and  use  one  pint  and  a  gill, 
how  many  gills  shall  I  then  have  ? 

Daisy  has  eight  clover  blossoms  in  her  hand ;  five  are 
red  and  the  rest  are  white ;  how  many  are  white  ? 

Eight  pansies  minus  five  pansies  are  how  many  pansies  ? 

Tell  me  stories  about  eight  minus  five. 

Write  :    Eight  minus  five  are  three. 


THE   NUMBER   EIGHT.  137 


Exercise   for  Review. 


One  robin,  two  swallows,  three  blue-birds,  and  two  jays, 
are  bow  many  birds  ? 

Two  hens,  three  turkeys,  and  three  ducks,  are  how  many 
fowls? 

Three  horses,  a  dog,  a  sheep,  and  three  cows,  are  how 
many  animals? 

Four  roses  and  three  lilies  are  how  many  flowers  ? 

Five  elms  and  three  maples  are  how  many  trees? 

Two  rose-bushes,  a  lilac-bush,  a  syringa,  and  three  flower- 
ing-almonds, are  how  many  shrubs  ? 

My  watch  is  five  seconds  slow ;  if  it  loses  three  more 
seconds,  how  slow  will  it  be  ? 

I  have  three  cents ;  how  many  more  cents  must  I  have 
to  have  eight  cents  ?  How  many  cents  do  I  need  to  have 
seven  cents? 

A  hen  had  eight  chickens,  but  the  cat  caught  two,  and 
one  got  drowned ;  how  many  had  she  then  ? 

I  had  a  two-cent  piece,  one  cent,  and  a  five-cent  piece ; 
how  many  cents  had  I  after  spending  five  cents? 

One  week  is  what  part  of  a  month  ? 

We  have  a  new  moon  every  month ;  how  many  new 
moons  will  there  be  in  seven  months  ? 

We  have  a  full  moon  every  month  ;  how  many  full  moons 
will  there  be  in  eight  months  ? 

How  many  dozen  buttons,  at  four  cents  a  dozen,  can  I 
buy  for  seven  cents?  and  how  many  cents  shall  I  have 
left? 

Two  horses  have  how  many  feet  ? 

Four  cows  have  how  many  horns  ? 

Four  baskets  have  how  many  handles,  if  each  basket 
has  two  handles  ? 


138  FIRST  STEPS   IN   NUMBER. 

In  making  a  picture-book  I  put  two  pictures  on  a  page ; 
how  many  pictures  can  I  put  on  two  leaves  ? 

What  four  equal  numbers  make  eight? 

What  two  equal  numbers,  and  two  more,  make  eight? 

I  have  seven  cards,  and  Annie  has  five ;  how  many  must 
I  give  Annie  so  that  each  of  us  may  have  the  same 
number? 

How  many  whole  dollars  are  there  in  six  half-dollars  ? 

Four  and  Four. 

You  have  four  fingers  on  one  hand,  without  your  thumb, 
and  four  on  the  other ;  how  many  fingers  have  you  without 
your  thumbs? 

Here  are  four  cups  and  four  saucers ;  how  many  dishes 
are  there  ? 

If  Jennie  wipes  four  knives  and  four  forks,  how  many 
things  does  she  wipe  ? 

This  card  has  four  dots  on  one  half,  and  four  dots  on  the 
other  half ;  how  many  dots  has  it  ? 

On  the  table  are  four  bottles  and  four  glass  stopples  ; 
how  many  things  are  on  the  table  ? 

In  the  jeweller's  Avindow  are  four  watches  and  four 
watch-cases ;  how  many  things  are  there  in  the  window  ? 

In  the  lower  sash  of  the  window  are  four  panes  of  glass, 
and  in  the  upper  sash  four  panes ;  how  many  panes  are  in 
the  window? 

Show  me  that  four  splints  and  four  splints  are  eight 
splints ;  that  four  spools  and  four  spools  are  eight  spools ; 
that  four  cents  and  four  cents  are  eight  cents ;  that  four  in 
on  one  line,  and  four  is  on  another  line,  are  eight  i's ;  that 
four  boxes  and  four  box-covers  are  oight  things. 

It  is  four  miles  to  the  foot  of  Mt.  Prospect ;  how  many 
miles  is  it  to  the  foot  of  Mt.  Prospect  and -back? 


THE   NUMBER   EIGHT.  139 

Four  little  girls  and  four  dolls  made  me  a  visit  one  day; 
how  many  made  me  a  visit  ? 

Tell  me  stories  about  four  and  four. 
Write :    Four  and  four  are  eight. 

Eight  minus  Four. 

I  have  eight  blocks ;  I  will  put  four  back  in  the  pile ; 
how  many  blocks  have  I  now  ? 

Nettie  may  take  eight  blocks,  and  give  four  to  John  ; 
how  many  blocks  has  Nettie  ? 

Mary  may  find  a  card  with  eight  dots  on  it ;  cover  four ; 
how  many  dots  can  you  see  ? 

Make  eight  dots  ;  erase  four ;  how  many  remain  ? 

Here  are  eight  chickens  in  the  yard  ;  four  run  to  me  for 
some  corn  ;  how  many  are  in  the  yard  now  ? 

The  cook  makes  eight  loaves  of  bread  a  day  ;  if  we  eat 
two  in  the  morning  and  two  at  noon,  how  many  are  left 
for  supper  ? 

There  are  eight  wheels  on  a  steam-car  ;  if  four  are  taken 
oiF,  how  many  are  on  the  car  ? 

There  are  eight  desks  in  a  row ;  if  four  have  no  books  in 
them,  how  many  have  books  ?  If  four  children  sit  in  the 
row,  there  is  room  for  how  many  more  children  ? 

If  I  have  eight  yards  of  ribbon,  and  use  four,  how  many 
yards  have  I  left  ? 

A  wooden  water-pail  holds  eight  quarts ;  if  it  has  four 
quarts  in  it,  how  many  more  quarts  will  it  hold  ? 

I  bought  four  quarts  of  berries  this  morning,  but  have 
used  four  pints  of  the  berries  ;  how  many  pints  have  I  left  ? 

I  have  eight  quarters  of  a  dollar ;  if  I  spend  four  quarters, 
how  many  quarters  have  I  to  spend  ?  how  many  dollars  ? 

I  had  eight  halves  of  a  dollar ;  I  used  four  halves ;  how 
many  halves  have  I  now  to  use  ?  how  many  dollars  ? 


140  FIRST   STEPS   IN   NUMBER. 

In  a  quart  pail  were  eight  gills  of  milk ;  we  used  four 
gills  for  breakfast ;  how  many  gills  were  left  ?  how  many 
pints  ?  what  part  of  a  quart  ? 

This  strip  of  paper  is  eight  inches  long ;  if  I  cut  off  four 
inches,  how  long  will  it  be  ? 

Eight  white  clouds  were  floating  in  the  sky  a  moment 
ago,  but  four  have  floated  out  of  sight ;  how  many  can  I 
see? 

Write  :    Eight  minus  four  are  four. 


Eight  divided  by  Four. 

Here  are  eight  pencils ;  give  four  to  as  many  children  as 
you  can. 

Try  it  with  eight  buttons ;  to  how  many  children  can 
you  give  four  buttons,  if  you  have  eight  buttons  ? 

Take  eight  cents ;  put  four  in  a  box ;  how  many  boxes 
does  it  take  ? 

Take  eight  crayons,  and  put  four  at  a  board ;  at  how 
many  boards  can  you  put  four  crayons,  if  you  have  eight  ? 

A  chair-maker  has  turned  out  eight  chair-legs ;  how 
many  chairs  will  they  supply  ? 

There  are  eight  stove-legs  on  the  floor  in  a  tin-shop ; 
how  many  stoves  can  the  eight  legs  supply  ? 

There  are  eight  horses  in  the  stable ;  how  many  four- 
horse  coaches  will  the  eight  horses  supply  ? 

I  have  eight  cents ;  how  many  four-cent  sticks  of  twist 
can  I  buy  ? 

A  gardener  had  eight  trees  to  set  out ;  he  put  four  in  a 
row ;  how  many  rows  did  he  set  out  ? 

There  are  eight  gills  of  vinegar  in  a  jug  ;  how  many  pints 
of  vinegar  are  in  the  jug? 

Write :    There  are  four  twos  in  eight. 


THE   NUMBER   EIGHT.  141 


T\vo  Fours. 


Take  four  blocks ;  take  another  four  blocks ;  how  many 
four-blocks  have  you  ?  how  many  blocks  ? 

Here  are  four  spools,  and  here  are  four  spools ;  how 
many  four-spools?  how  many  spools? 

Show  me  two  boxes  with  four  cents  in  each  box ;  how 
many  cents  do  you  show  me  ? 

How  many  feet  have  two  dogs  ? 

How  many  paws  have  two  kittens  ? 

How  many  wheels  have  two  four-wheeled  carriages  ? 

How  many  gills  in  two  pints  ? 

How  many  "inches  in  two  strips  of  card  each  four  inches 
long? 

How  many  fourths  in  two  whole  ones  ? 

If  you  have  four  miles  to  ride,  and  I  have  twice  as  far, 
how  far  have  I  to  ride  ? 

If  Lizzie  must  copy  four  words,  and  Victor  twice  as 
many  words,  how  many  words  must  Victor  copy  ? 

Tell  me  stories  about  two  fours. 

Write  :    Two  fours  are  eight. 

Exercise  for  Review. 

If  it  takes  six  yards  of  carpeting  for  a  hall  that  is  three 
yards  long,  how  wide  is  the  hall  ? 

Three  quarts  and  a  half  of  berries  are  how  many  pints  of 
berries  ? 

Three  pounds  and  a  half  of  potatoes,  at  two  cents  a  pound, 
cost  how  much  ? 

In  two  months  how  many  weeks? 

In  two  months  how  many  moons  ? 

Four  cakes  cost  eight  cents ;  what  will  two  cakes  cost  ? 


142  FIRST   STEPS    IN   NUMBER 

How  many  bananas,  at  five  cents  each,  can  you  buy 
for  eight  cents,  and  how  many  cents  will  you  have  toward 
buying  another  banana?  How  many  bananas  at  the 
same  price  could  you  buy  for  seven  cents,  and  how  many 
cents  would  you  have  toward  buying  another  ? 

How  many  strokes  does  the  town  clock  give  from  half- 
past  two  to  half-past  four  ? 

Letters  are  now  carried  for  three  cents ;  next  year  they 
will  be  carried  for  two  cents ;  how  much  money  will  then 
be  saved  in  sending  six  letters  ? 

Four  two-horse  sleds  have  just  passed  ;  how  many  horses 
did  it  take  to  draw  them  ?  How  many  drivers,  if  there 
was  a  driver  for  each  sled  ?  If  each  driver  had  charge  of 
two  sleds,  how  many  drivers  would  four  sleds  require? 

How  many  runners  had  the  four  sleds? 

How  many  stakes  had  each  sled,  if  there  were  four  stakes 
on  a  side?     How  many  runners  has  a  double-runner? 

If  a  man  lays  two  feet  of  wall  in  a  day,  how  long  will  it 
take  him  to  lay  eight  feet  of  wall  ?  If  two  men  lay  four 
feet  of  wall  in  a  day,  how  long  will  it  take  them  to  lay 
eight  feet  ? 

Name  two  equal  numbers  that  m.ake  eight. 

Name  two  equal  numbers  and  two  that  make  eight. 

Name  eight  equal  numbers  that  make  eight. 

A  little  iron  rake  had  eight  teeth,  but  four  got  broken 
out ;  how  many  did  the  rake  then  have  ? 

How  many  handles  have  four  plows  ? 

A  pitchfork  has  four  tines;  how  many  tines  have  two 
such  pitchforks  ? 

A  man  could  get  only  a  half  cord  of  wood  each  time ; 
how  many  times  would  he  need  to  go  to  get  four  cords? 

How  many  shafts  have  three  wagons? 

An  ox  has  two  toes  on  each  foot ;  how  many  toes  has  he 
altogether  ? 


THE   NUMBER   EIGHT.  143 

An  ox  wears  two  shoes  on  each  foot ;  how  many  shoes 
does  he  wear  ? 

A  blacksmith  has  eight  horseshoes ;  how  many  horses 
can  he  shoe  all  round  ? 

There  are  two  heads  to  a  barrel ;  how  many  heads  have 
four  barrels,  if  one  barrel-head  is  gone  ? 


Eight  minus  Eight. 

There  are  eight  children  about  the  table ;  eight  children 
may  sit  on  the  platform ;  how  many  children  are  now  about 
the  table  ? 

Here  are  eight  spoons ;  you  may  put  eight  spoons  in  the 
box ;  how  many  spoons  remain  out  of  the  box  ? 

There  are  eight  buttons  on  your  boot ;  if  eight  buttons 
come  off  of  your  boot,  how  many  will  there  be  on  the 
boot? 

There  are  eight  buttons  on  your  jacket ;  if  mamma  cuts 
off  eight  buttons,  how  many  buttons  will  there  be  on  your 
jacket? 

Johnnie  filled  eight  baskets  with  leaves,  but  Albert 
tipped  over  eight  baskets  and  scattered  the  leaves ;  how 
many  were  then  filled  with  leaves? 

Willie's  uncle  gave  him  eight  dollars ;  Willie  put  eight 
dollars  in  the  bank  ;  how  many  dollars  had  he  beside  ? 

In  a  show-window  there  were  eight  doll-cradles,  but 
eight  of  them  were  sold  ;  how  many  were  left  to  sell  ? 

There  are  eight  things  in  my  pencil-tray  ;  if  I  take  eight 
things  out  of  the  tray,  how  many  things  remain  in  the  tray  ? 

Eddie  had  eight  cookies ;  when  he  had  eaten  eight 
cookies,  how  many  cookies  had  he  to  eat  ? 

Tell  me  stories  about  eight  minus  eight. 

Write  :    Eight  minus  eight  are  none. 


144  FIRST  STEPS   IN   NUMBER. 

Eight  divided  by  One. 

Take  eight  cups ;  put  each  in  a  saucer ;  how  many  saucers 
does  it  take  for  the  eight  cups  ? 

Take  eight  spoons ;  put  each  in  a  cup ;  how  many  cups 
does  it  take  for  the  eight  spoons  ? 

Take  eight  pencils ;  give  one  to  each  of  as  many  children 
as  you  can ;  to  how  many  children  can  you  give  one  pencil 
each,  if  you  have  eight  pencils  ? 

To  how  many  children  can  the  salesman  sell  eight  slates, 
if  he  sells  one  to  each  child  ? 

Eight  hooks  will  be  enough  for  how  many  pictures,  if  one 
hook  is  enough  for  one  picture  ? 

Eight  cents  will  buy  how  many  one-cent  books?  how 
many  one-cent  stamps?  how  many  one-cent  pencils? 

Eight  horses  will  take  how  many  stalls,  if  one  horse  takes 
one  stall  ? 

Tell  me  stories  about  eight  divided  by  one. 

Write :    There  are  eight  ones  in  eight. 

Eight  Ones. 

How  many  handles  have  eight  knives  ? 

How  many  seats  have  eight  chairs  ? 

How  many  tops  have  eight  tables  ? 

How  many  trunks  have  eight  elephants  ? 

Eight  birds  have  how  many  bills  ? 

Eight  windows  have  how  many  shades? 

Eight  rooms  have  how  many  ceilings  ? 

Eight  mirrors  have  how  many  frames  ? 

Eight  men  were  going  into  the  woods  to  work ;  the  far- 
mer's wife  put  up  a  lunch  for  each ;  how  many  lunches 
did  she  put  up  ? 

How  many  stamps  will  be  required  for  eight  letters,  if 
each  letter  requires  one  stamp  ? 


THE   NUMBER   EIGHT.  145 

How  many  times  does  the  girl  go  to  tlie  market,  if  she 
goes  once  a  day  for  eight  days  ? 

If  we  eat  a  pound  of  oatmeal  each  day,  how  many  pounds 
shall  we  eat  in  eight  days  ? 

Tell  me  stories  for  eight  ones. 

Write  :    Eight  ones  are  eight. 

Eight  divided  by  Eight. 

How  many  ones  can  you  find  in  eight  ? 

How  many  twos  can  you  find  in  eight  ? 

How  many  fours  can  you  find  in  eight  ? 

How  many  eights  can  you  find  in  eight  ? 

If  you  had  eight  fish-hooks,  to  how  many  boys  could  you 
sell  a  fish-hook  ? 

How  many  eight-cent  watches  can  you  buy  for  eight 
cents  ? 

A  gardener  setting  out  trees,  sets  eight  in  a  row ;  how 
many  rows  can  he  make  from  eight  trees  ? 

A  large  oven  will  hold  eight  pies;  how  many  times 
must  the  cook  bake  to  bake  eight  pies  ? 

How  many  eight-cent  loaves  of  bread  can  you  buy  for 
eight  cents  ? 

If  crackers  are  eight  cents  a  dozen,  how  many  dozen 
crackers  can  be  bought  for  eight  cents  ? 

Tell  me  stories  for  eight  divided  by  eight. 

Write  :    There  is  one  eight  in  eight. 

Halves  of  Eight. 

Take  eight  blocks  ;  divide  them  into  halves. 

Show  me  one-half  of  eight  blocks ;  how  many  blocks  are 
one-half  x)i  eight  blocks  ? 

Find  one-half  of  eight  baskets ;  how  many  baskets  are 
one-half  of  eight  baskets  ? 


146  FIRST   STEPS   IN   NUMBER. 

Show  me  one-half  of  eight  buttons ;  how  many  buttons 
are  a  half  of  eight  buttons  ? 

How  many  cards  are  one-half  of  eight  cards  ? 

How  many  newspapers  are  one-half  of  eight  newspapers? 

How  many  apples  are  one-half  of  eight  apples  ? 

I  have  eight  kittens ;  if  I  give  away  half  of  them,  how 
many  kittens  shall  I  give  away  ? 

I  spent  four  cents  this  morning,  which  is  half  the  money 
I  had  ;  how  much  money  had  I  ? 

Johnnie,  who  is  four  years  old,  is  half  as  old  as  George ; 
how  old  is  George  ? 

There  are  eight  gills  in  a  quart ;  how  many  gills  in  half 
a  quart? 

Rice  is  eight  cents  a  pound ;  what  will  half  a  pound  of 
rice  cost  ? 

Four  miles  is  half  the  distance  home ;  what  is  the  dis- 
tance home  ? 

When  four  of  the  lamps  in  a  chandelier  are  lighted,  half 
of  the  lamps  are  lighted  ;  how  many  lamps  has  the  chande- 
lier? 

Four  is  one-half  what  number  ? 

Eight  is  twice  what  number  ? 

Show  me  two  halves  of  eight  blocks. 

Which  had  you  rather  have,  eight  oranges  or  two  halves 
of  eight  oranges  ? 

Which  is  the  more  jelly,  eight  cups  of  jelly  or  two  halves 
of  eight  cups  of  jelly  ? 

A  man  who  had  eight  horses,  sold  half  his  horses ;  how 
many  horses  did  he  sell  ? 

When  the  hour-hand  is  one-half  the  distance  from  twelve 
to  eight,  to  what  figure  does  it  point  ? 

I  had  'eight  letters  to  write  ;  I  have  written  four  ;  what 
part  of  eight  have  I  written  ? 

Write  :    One-half  of  eight  is  four. 


THE   NUMBER   EIGHT.  147 


Fourths  of  Eight. 

Put  eight  blocks  into  four  equal  groups.  How  many  in 
each  group  ? 

What  part  of  eight  is  each  group  ? 

How  many  blocks  in  a  fourth  of  eight  blocks  ?  Show  me 
a  fourth  of  eight  buttons ;  how  many  buttons  do  you  show 
me? 

Arrange  eight  children  in  rows  so  that  a  fourth  of  them 
will  be  in  each  row. 

Put  eight  books  in  piles  so  that  a  fourth  of  them  will  be 
in  each  pile. 

Arrange  eight  dots  in  rows  so  that  a  fourth  of  eight  dots 
will  be  in  each  row. 

Put  eight  shells  in  boxes  so  that  a  fourth  of  them  will  be 
in  each  box ;  how  many  shells  in  each  box  ? 

I  divided  eight  picture-books  equally  among  four  chil- 
dren; how  many  books  did  I  give  to  each  child?  what  part 
of  eight  did  I  give  to  each  ? 

A  boy  who  earned  eight  dollars  a  week,  saved  a  fourth 
of  it  each  week ;  how  much  did  he  save  ? 

A  little  girl  who  had  eight  cents,  spent  a  fourth  of  her 
money  for  a  pencil ;  how  much  did  the  pencil  cost  ? 

Irene  had  eight  weeks'  vacation ;  she  spent  a  fourth  of 
her  vacation  at  the  beach ;  how  many  weeks  did  she  stay 
at  the  beach  ? 

How  many  weeks  in  a  fourth  of  two  months  ? 

How  many  gills  in  a  fourth  of  a  quart  ? 

I  cut  an  apple  into  eight  pieces;  if  I  gave  Alice  two 
pieces,  what  part  of  the  whole  number  of  pieces  did  I  give 
her? 

There  were  eight  roses  on  a  bush  ;  two  fell  off ;  what 
part  of  the  whole  number  of  roses  fell  off? 


148  FIRST  STEPS   IN   NUMBER. 

Eight  boys, were  drilling  in  a  military  company;  two 
were  ordered  out  of  the  line  for  not  paying  attention  ;  what 
part  of  the  whole  number  was  ordered  out  ? 

It  is  eight  miles  to  a  certain  lake ;  if  I  walk  two  miles, 
what  part  of  the  distance  do  I  walk  ? 

A  tin-peddler  travels  eight  miles  a  day  ;  what  part  of  the 
distance  has  he  gone  when  he  has  travelled  two  miles  ? 

In  a  figure  which  Willie  designed  with  splints,  there  were 
eight  triangles ;  how  many  triangles  were  there  in  a  fourth 
of  the  design  ? 

Tell  me  what  part  of  eight  dots  I  make  on  the  board. 
Tell  me  what  part  of  eight  cents  I  show  you.  Tell  me 
what  part  of  eight  nuts  I  put  in  the  drawer;  how  many  nuts? 

A  boy  earned  eight  dollars  in  four  weeks ;  how  many 
dollars  did  he  earn  a  week  ? 

Annie  can  write  eight  stories  in  four  minutes  ;  how  many 
stories  does  she  write  a  minute  ? 

Four  pairs  of  boots  cost  eight  dollars ;  how  many  dollars 
a  pair  do  they  cost  ? 

Four  erasers  cost  eight  cents  ;  what  does  one  eraser  cost  ? 

Four  pairs  of  silk  mittens  cost  eight  dollars ;  what  is  the 
price  of  a  pair  ? 

What  is  one-fourth  of  eight? 

Two  is  one-fourth  of  what  number  ? 

One-fourth  of  eight  is  how  many  ? 

Show  me  two-fourths  of  eight  splints. 

How  many  splints  are  two-fourths  of  eight  splints  ? 

Show  me  three-fourths  of  eight  splints. 

How  many  splints  are  three-fourths  of  eight  splints  ? 

Show  me  four-fourths  of  eight  splints. 
••  Which    is  more,   eight  splints  or  four-fourths  of  eight 
splints  ? 

If  the  cook  uses  one-fourth  of  eight  eggs  each  day,  how 
many  fourths  of  eight  eggs  will  she  use  in  four  days  ?  how 
many  eggs  ? 


THE   NUMBER  EIGHT.  149 

If  each  person  eats  one-fourth  of  eight  eggs  for  break- 
fast, how  many  eggs  do  four  persons  eat? 

Eight  minus  one-fourth  of  eight  are  how  many  ? 
Eight  minus  two-fourths  of  eight  are  how  many  ? 
Eight  minus  one-half  of  eight  are  how  many  ? 
Write  :    One-fourth  of  eight  is  two. 


§  26.   Comparison  of  Eight  with  Numbers  Known. 

At  Eoy's  house  are  eight  kittens  and  eight  puppies  ;  how 
many  more  kittens  are  there  than  puppies  ? 

At  the  Zoological  Gardens  there  were  eight  bears  and 
eight  seals ;  how  many  more  bears  than  seals  were  there  ? 

Find  how  many  more  there  are  in  eight  than  in  seven. 

If  there  were  eight  boats  going  down  the  river,  and 
seven  going  up  the  river,  how  many  more  boats  were 
going  down  the  river? 

If  there  were  eight  honey-bees,  and  only  seven  honey- 
suckle blossoms,  would  there  be  a  blossom  for  each  bee? 
how  many  bees  would  have  to  fly  to  another  flower  ? 

Harry  has  eight  figs,  Louise  seven  figs  ;  how  many  more 
figs  has  Harry  than  Louise  ? 

Find  how  many  more  there  are  in  eight  than  in  six. 

How  many  more  legs  have  two  oxen  than  three  boys  ? 

How  many  more  legs  have  two  chairs  than  two  three- 
legged  stools  ? 

I  have  four  two-cent  coins ;  Mary  has  two  three-cent 
coins ;  how  much  more  money  have  I  than  Mary  ? 

Four  two-horse  sleds  will  require  how  many  more  horses 
than  six  single-horse  sleds? 

Eight  boys  are  raking  hay ;  six  men  are  mowing ;  how 
many  more  boys  than  men  are  there  in  the  hay-field  ? 

Find  how  many  more  there  are  in  eight  than  in  five. 


150  FIRST   STEPS   IN   NUMBER. 

I  have  eight  daisies  and  five  violets ;  how  many  more 
daisies  than  violets  have  I  ? 

Eight  boys  were  playing  polo  ;  five  were  looking  on  ; 
how  many  more  were  playing  than  looking  on  ? 

There  were  eight  mice  in  a  basket,  and  five  kittens 
all  ready  to  eat  them ;  how  many  more  mice  than  kittens 
were  there  ? 

I  have  two  three-cent  pieces  and  two  cents  in  my  purse, 
and  a  five-cent  piece  in  my  hand  ;  how  much  more  have  I 
in  my  purse  than  in  my  hand  ? 

Find  how  many  more  there  are  in  eight  than  in  four. 

How  many  more  wheels  has  a  steam-car  than  a  carriage  ? 

Two  chairs  have  how  many  more  legs  than  one  chair  ? 

Eight  horses  have  how  many  more  heads  than  four 
horses  ? 

Two  squares  have  how  many  more  sides  than  one  square? 

Find  how  many  more  there  are  in  eight  than  in  three. 

This  room  is  eight  feet  high  ;  this  little  girl  is  only  three 
feet  high ;  how  much  higher  is  the  room  than  Blanche  ? 

A  cat,  a  rooster,  and  a  donkey  agreed  to  travel  together ; 
they  overtook  eight  robbers ;  how  many  more  were  in  one 
company  than  in  the  other  ? 

I  skated  three  times  across  the  pond  ;  Florence  skated 
eight  times  across  the  pond ;  how  many  more  times  did 
Florence  skate  across  the  pond  than  I  ? 

Two  men  were  selling  balloons ;  one  had  sold  all  but 
eight ;  the  other  had  sold  all  but  three ;  how  many  more 
had  one  to  sell  than  the  other  ? 

Find  how  many  more  there  are  in  eight  than  in  two. 

One  dog  had  eight  bones  thrown  out  to  hini ;  another 
had  only  two  bones ;  how  many  more  bones  did  one  have 
than  the  other? 

How  many  more  gills  are  there  in  a  cjuart  than  in  a  tea- 
cup, if  the  tea-cup  holds  two  gills  ? 


THE   NUMBER   EIGHT.  151 

How  many  more  shoes  does  an  ox  wear  than  you  ? 

Find  how  many  more  there  are  in  eight  than  in  one. 

A  cabinet-maker  made  eight  tables  with  drawers,  and 
one  without ;  how  many  more  did  he  make  with  drawers 
than  without? 

There  are  two  card-baskets  on  the  table ;  one  has  eight 
cards  in  it,  the  other  has  only  one  card  ;  how  many  more 
cards  has  one  basket  than  the  other? 

In  one  fruit-dish  there  are  eight  clusters  of  grapes ;  in 
another  one  cluster ;  how  many  more  clusters  are  there  in 
one  dish  than  in  the  other? 

Eight  is  how  many  more  than  one  ? 

One  is  how  many  less  than  eight  ? 

Eight  is  how  many  more  than  seven  ? 

Seven  is  how  many  less  than  eight  ? 

Eight  is  how  many  more  than  two  ? 

Two  is  how  many  less  than  eight? 

Eight  is  how  many  more  than  six  ? 

Six  is  how  many  less  than  eight  ? 

Eight  is  how  many  more  than  three  ? 

Three  is  how  many  less  than  eight? 

Eight  is  how  many  more  than  five  ? 

Five  is  how  many  less  than  eight  ? 

Eight  is  how  many  more  than  four  ? 

Four  is  how  many  less  than  eight  ? 

Charley  has  eight  rabbits ;  Bennie  has  half  as  many ; 
how  many  more  rabbits  has  Charley  than  Bennie  ? 

In  one  hand  I  have  four  two-cent  pieces ;  in  the  other 
hand  I  have  only  half  as  many  two-cent  pieces  ;  how  many 
more  cents  are  there  in  one  hand  than  in  the  other  ? 

There  were  eight  of  us  when  we  were  children  at  home ; 
there  were  half  as  many  cousins  in  the  house  opposite ; 
how  many  more  of  us  were  there  than  cousins  in  the  house 
opposite  ? 


152  FIRST  STEPS   IN   NUMBER. 

This  line  i^  eight  inches  long ;  this  short  line  is  only 
one-fourth  as  long ;  how  much  longer  is  one  line  than  the 
other? 

Eight  children  are  playing  "Eing  around  Rosy";  one- 
fourth  of  that  number  are  playing  ball ;  how  many  more 
are  playing  in  the.  ring  ? 

One  and  how  many  are  eight? 

Seven  and  how  many  are  eight  ? 

Two  and  how  many  are  eight  ? 

Six  and  how  many  are  eight  ? 

Three  and  how  many  are  eight  ? 

Five  and  how  many  are  eight  ? 

Four  and  how  many  are  eight  ? 

Eight  and  how  many  are  eight  ? 

Eight  minus  one  are  how  many  ? 

Eight  minus  seven  are  how  many  ? 

Eight  minus  two  are  how  many  ? 

Eight  minus  six  are  how  many  ? 

Eight  minus  three  are  how  many  ? 

Eight  minus  five  are  how  many  ? 

Eight  minus  four  are  how  many  ? 

How  many  fours  in  eight? 

How  many  twos  in  eight? 

How  many  ones  in  eight? 

One-half  of  eight  is  how  many  ? 

One-fourth  of  eight  is  how  many  ? 

One-eighth  of  eight  is  how  many  ? 

Four  blocks  are  what  part  of  eight  blocks  ? 

Two  blocks  are  what  part  of  eight  blocks  ? 

One  is  what  part  of  eight  ? 


CHAPTER   VIIL 

THE    NUMBER    NINE. 


§27.     Nine  as  a  Whole. 

Take  eight  blocks ;  put  one  more  block  with  them.  Show 
me  just  as  many  paper  disks  ;  as  many  splints ;  as  many 
shells  ;  as  many  pebbles ;  as  many  paper  patterns ;  as  many 
dots  on  the  board  ;  as  many  lines  on  the  board  ;  as  many  i8 
on  the  board.  You  have  shown  me  nine  z's.  How  many 
lines  have  you  shown  me?  how  many  dots?  how  many 
splints?  how  many  blocks?  Find  nine  bits  of  crayon. 
Mary,  collect  nine  pencils  from  the  desks.  Harry,  pick  out 
nine  cents.  Annie,  put  nine  cups  in  a  row.  Georgie,  find 
nine  saucers  to  go  with  these  cups.  Alice,  find  a  card  with 
nine  dots  on  it.     Fannie,  pick  out  nine  paper  spoons. 

Who  thinks  there  are  as  many  as  nine  desks  in  two  rows 
of  desks?  that  there  are  as  many  as  nine  rounds  on  the 
back  of  the  settee  ?  that  there  are  as  many  as  nine  figures 
on  the  clock  ? 

Mention  the  things  in  this  room  of  which  there  are  at 
least  nine. 

Name  nine  different  things  you  see  in  this  room.  Name 
again. 

Arrange  nine  dots  on  the  board  in  all  the  ways  you 
can. 

Mention  things  of  which  you  would  see  nine  on  the 
street ;  in  your  homes. 


154  FIRST  STEPS   IN   NUMBER. 

Name  nine  different  things  you  saw  on  your  way  to 
school  this  morning,  and  take  a  block  for  each  one. 

Each  take  nine  splints;  see  how  many  designs  can  be 
made  using  the  nine  splints  each  time. 


§  28.   Discoveries  in  Nine. 

Take  nine  blocks.  Each  show  me  two  numbers  that 
together  make  nine.  Tell  me  what  you  have  found.  Find 
again  ;  tell  me  what  you  have  found. 

Each  take  a  number  out  of  nine.  Tell  me  what  you 
have  taken  away,  and  what  remains.  Try  it  again,  and 
tell  me  what  you  have. 

Separate  nine  into  equal  groups,  and  tell  me  what  you 
have. 

See  if  you  can  separate  nine  into  halves ;  into  fourths. 

Find  what  you  must  put  with  eight  to  make  nine ;  with 
seven ;  with  six ;  with  five ;  with  four ;  with  three ;  with 
two  ;  with  one  ;  with  none. 

What  number  taken  from  nine  will  leave  one  ?  will  leave 
two  ?  will  leave  three  ?  four  ?  five  ?  six  ?  seven  ?  eight  ? 

Copy  the  word  nine  on  your  slates. 


§29.   Facts  in  Nine. 
Eight  and  One. 

Illustrate  the  story  I  tell  you  with  blocks.  Eight 
chickens  were  eating  out  of  a  dish,  and  one  more  chicken 
came  to  eat  with  them ;  how  many  chickens  were  then 
eating  out  of  the  dish  ? 

Illustrate  again.  There  were  eight  little  mice  in  a  nest, 
and  the  mother  mouse  ;  how  many  were  there  in  all  ? 


THE   NUMBER   NINE.  155 

There  were  eight  swallows'  nests  in  a  sand-bank,  and  one 
more  nest  was  built.  How  many  nests  were  then  in  the 
sand-bank  ? 

Eight  children  were  playing  tag,  afiid  one  more  child 
joined  them ;  how  many  were  then  playing  tag  ? 

Eight  morning-glories  were  blossomed  early  this  morn- 
ing, and  one  more  morning-glory  blossomed  out  before  I 
came  to  school ;  how  many  blossoms  were  then  on  the  vine  ? 

I  paid  eight  cents  for  a  book,  and  one  cent  for  a  pencil ; 
how  much  did  I  pay  for  both  ? 

There  were  eight  pictures  in  my  scrap-book,  and  I  have 
just  put  one  more  picture  in  it ;  how  many  pictures  are  now 
in  my  scrap-book  ? 

I  have  eight  pictures  in  my  room  ;  how  many  shall  I  have 
if  I  buy  one  picture  more  ? 

Eddie  has  eight  story  books ;  how  many  will  he  have  if 
another  story  book  is  given  him  ? 

You  have  been  to  school  eight  months  this  year ;  if  you 
go  another  month,  how  many  months  will  you  have  been 
to  school  ? 

Tell  me  a  story  about  eight  quarts  of  blackberries  and 
one  quart  of  blackberries ;  eight  currant  bushes  and  one 
currant  bush ;  eight  pounds  of  butter  and  one  pound  of 
butter ;  eight  pans  of  milk  and  one  pan  of  milk ;  eight 
rows  of  trees  and  one  row  of  trees ;  eight  robins  and  one 
bluebird ;  eight  roses  and  one  tulip ;  eight  cows  and  one 
horse  ;  eight  hand-rakes  and  one  horse-rake. 

Write  :  Eight  and  one  are  nine. 


One  and  Eight. 

Show  me  one  block ;  show  me  eight  blocks  more ;  how 
many  blocks  have  you  shown  me  ? 

Tell  me  a  story  for  what  you  have  shown  me. 


156  FIRST   STEPS   IN   NUMBER. 

One  sunbeam  played  through  a  hole  in  the  roof  of  the 
barn,  and  soon  eight  more  sunbeams  came  too ;  how  many 
sunbeams  then  lighted  the  barn  ? 

At  one  place  under  the  eaves  was  a  swallow's  nest,  and 
at  another  place  there  were  eight  nests ;  how  many  nests 
were  there  in  all  ? 

Willie  found  one  egg  in  one  nest,  and  eight  eggs  in 
another  nest ;  how  many  eggs  did  he  find  ? 

If,  in  the  end  of  a  house  there  is  one  window  under  the 
eaves,  and  eight  more  windows  below  it,  how  many  windows 
in  all? 

I  have  one  nut  in  my  hand ;  if  you  give  me  eight  nuts 
more,  how  many  nuts  shall  I  have  ? 

The  cook,  in  making  an  apple  pudding,  put  one  apple 
in  the  middle  of  the  dish,  and  eight  apples  around  it; 
how  many  apples  did  she  put  in  the  dish? 

One  little  boy  wished  to  play  with  the  blocks,  and  then 
eight  more  boys  wanted  to  play  with  them ;  how  many 
boys  wanted  to  play  with  the  blocks  ? 

Harry's  mother  told  him  he  might  go  nutting  if  he  could 
get  any  boys  to  go  with  him.  He  found  eight  boys  who 
could  go ;  how  many  boys  were  there  in  all  to  go  nutting  ? 

One  sheep  jumped  over  the  fence,  and  so  eight  more 
sheep  jumped  over  the  fence  ;  how  many  sheep  jumped 
over  the  fence  ? 

Write :  One  and  eight  are  nine. 

Nine   minus  One. 

Stand  nine  spools  in  a  row.  Call  them  soldiers.  One 
soldier  got  out  of  line  ;  how  many  soldiers  were  left  in  line  ? 

Call  them  lamp-posts.  One  lamp-post  had  no  lamp  on 
it ;  how  many  lamp-posts  had  lamps  ? 

Call  them  ninepins.  One  ninepin  tumbled  over;  how 
many  ninepins  were  left  standing  ? 


THE   NUMBER   NINE.  157 

Call  them  chimneys  a  mason  had  to  build.  He  built 
one  chimney  ;  how  many  more  chimneys  had  he  to  build  ? 

Call  them  lamp-chimneys.  One  lamp-chimney  got 
broken ;    how  many  lamp-chimneys  were  left  ? 

Call  them  gate-posts.  One  gate-post  fell  over;  how 
many  gate-posts  remained  standing  ? 

Call  them  pencils  I  must  sharpen.  If  I  sharpen  one 
pencil,  how  many  more  pencils  remain  to  be  sharpened  ? 

Call  them  pumps  which  a  pump-maker  had  to  sell.  He 
sold  one  pump ;  how  many  pumps  had  he  left  ? 

Call  them  weather-vanes.  One  weather-vane  blew  over  ; 
how  many  weather-vanes  were  there  then  ? 


Nine  minus  Eight. 

Make  nine  dots  on  the  board.  Draw  a  line  through 
eight  of  them  ;  how  many  more  dots  are  there  ? 

Draw  nine  straight  up-and-down  lines.  Erase  eight ; 
how  many  are  left  ? 

Draw  nine  right-and-left  lines.  Cover  eight  of  the  lines 
with  your  hand  ;  how  many  lines  do  you  see  now  ? 

Show  me  nine  blocks  minus  eight  blocks. 

There  were  nine  apples  in  the  fruit-dish  this  morning, 
but  eight  have  been  eaten  ;  how  many  are  left  ? 

Nine  doves  were  in  the  walk  picking  up  crumbs.  When 
I  opened  the  door,  eight  of  them  flew  away ;  how  many 
were  then  in  the  walk  ? 

A  hen  had  nine  chickens,  but  they  went  into  the  wet 
grass  and  eight  died  ;  how  many  chickens  were  there  then  ? 

There  were  nine  hacks,  at  the  station.  Eight  of  them 
had  passengers ;  how  many  had  none  ? 

There  were  nine  pigs  in  the  pen,  eight  got  out  of  the 
pen,  how  many  remained  in  the  pen  ? 


158  FIRST   STEPS   IN   NUMBER. 

I  have  nine  books  to  cover.  When  I  have  covered 
eight,  how  many  more  will  there  be  to  cover  ? 

If  there  are  nine  pins  on  the  cushion,  and  I  use  eight, 
how  many  will  there  be  on  the  cushion  ? 

"Who  will  tell  me  a  story  for  nine  minus  eight  ?  Another 
story  ?  another  ?  another  ? 

Write  :    Nine  minus  eight  is  one. 

Exercise  for  Review. 

Show  me  four  blocks ;  six  blocks ;  five  blocks ;  seven 
blocks  ;  nine  blocks ;  eight  blocks. 

Tell  the  number  I  show  you.     Again  ;  again. 

Find  how  many  twos  in  four.  Give  me  a  story  for  four 
divided  by  two. 

Find  how  many  twos  in  six.  Give  me  a  story  for  six 
divided  by  two. 

Find  how  many  twos  in  eight.  Give,  me  a  story  for 
eight  divided  by  two. 

Show  me  eight,  in  twos.     How  many  twos  ? 

Tell  me  a  story  for  four  twos  are  eight. 

Show  me  six,  in  twos.     How  many  twos? 

Give  me  a  story  for  three  twos  are  six. 

Show  me  six,  in  threes.     How  many  threes  ? 

Give  me  a  story  for  two  threes  are  six. 

Harry  had  six  arrows  for  his  bow,  but  has  shot  two ; 
how  many  has  he  left  ?  If  he  had  shot  four,  how  many 
would  have  remained  ? 

If  he  has  four  arrows,  and  makes  two  more,  how  many 
arrows  will  he  have  ? 

If  he  loses  all  but  two  of  these  arrows,  how  many  will 
he  lose?  If  then  he  buys  four  more,  how  many  will  he 
have? 

Six  pencils  minus  four  pencils  are  how  many  pencils  ? 


THE   NUMBER   NINE.  159 

Six  pencils  minus  two  pencils  are  how  many  pencils  ? 

Four  pencils  and  two  pencils  are  how  many  pencils  ? 

Two  pencils  and  four  pencils  are  how  many  pencils  ? 

Write  on  the  board :    Six  minus  four  are  two. 

Write  :  Six  minus  two  are  four. 

Write  :  Four  and  two  are  six. 

Write  :  Two  and  four  are  six. 

If  John  has  for  a  team  of  horses,  the  kitten,  a  cloth 
elephant,  two  wooden  horses,  and  a  pair  of  boots,  how 
many  horses  has  he  ? 

If  there  are  two  kittens  on  the  table,  one  kitten  in  a 
chair,  and  three  kittens  on  the  floor,  how  many  kittens  are 
there  in  all  ? 

There  were  seven  little  boys  dressed  as  soldiers ;  two 
had  flags  ;  how  many  did  not  have  flags  ? 

Jamie  had  seven  rabbits,  but  gave  two  away ;  how  many 
had  he  then  ? 

Nellie's  writing-book  cost  seven  cents.  She  had  only 
five  cents  ;  how  many  more  cents  did  she  need  to  pay  for  it? 

If  she  had  only  two  cents,  how  many  more  cents  would 
she  need? 

A  five-cent  piece  and  a  two-cent  piece  are  how  many 
cents  ? 

Write  on  the  board :  Five  and  two  are  seven. 

Write  :  Two  and  five  are  seven. 

Write  :  Seven  minus  two  are  five. 

Write  :  Seven  minus  five  are  two. 

There  were  four  ducks  in  the  pond,  and  three  on  the 
edge  of  the  pond  ;  how  many  were  there  in  all  ? 

There  were  three  mice  in  the  pantry,  and  four  more 
came  to  join  the  fun ;  how  many  mice  were  then  in  the 
pantry  ? 

My  lamp  will  burn  seven  hours.  After  it  has  burned 
three  hours,  how  many  more  hours  will  it  burn  ? 


160  FIRST  STEPS   IN   NUMBER. 

After  it  has  burned  four  hours,  how  long  will  it  burn  ? 

There  were  seven  yachts  in  the  harbor ;  three  were 
moored  ;  how  many  were  sailing  about  ? 

There  were  seven  roses  on  my  rose-bush,  but  I  cut  off 
four  this  morning ;  how  many  were  left  on  the  bush  ? 

Four  and  how  many  are  seven  ? 

Three  and  how  many  are  seven  ? 

Seven  minus  three  are  how  many  ? 

Seven  minus  four  are  how  many  ? 

Show  me  one-half  of  four.  One-half  of  six.  One-half  of 
eight. 

Show  me  one-fourth  of  four.     One-fourth  of  dght. 

It  is  four  miles  from  Boston  to  Mount  Auburn ;  how  far 
is  it  half-way  to  Mount  Auburn  ? 

I  teach  six  hours  a  day ;  how  many  hours  do  I  teach  in 
half  a  day  ? 

If  I  cut  a  pie  into  eight  equal  pieces,  how  many  pieces 
will  there  be  in  half  the  pie  ? 

If  I  cut  an  apple  into  four  equal  pieces,  what  part  of 
the  apple  is  each  piece  ? 

If  I  have  four  apples,  and  give  you  one-fourth  of  the 
number  I  have,  how  many  apples  shall  I  give  you  ? 

If  I  give  you  two-fourths,  how  many  shall  I  give  you  ? 
If  I  give  you  three-fourths  ?     If  I  give  you  four-fourths  ? 

I  had  eight  cents  in  my  pocket,  but  I  spent  a  fourth  of 
my  money ;  how  much  money  have  I  left  ? 

Ed  had  eight  hens,  but  sold  a  fourth  of  the  number  he 
had  ;  how  many  had  he  left  ? 

Etta  found  eight  eggs,  but  she  broke  a  fourth  of  them ; 
she  then  found  half  as  many  more  as  she  had  left;  how 
many  had  she  then  ? 

I  had  eight  blossoms  on  my  geranium,  but  a  fourth  of 
them  fell  to  pieces,  and  I  cut  off  half  of  what  remained ; 
how  many  blossoms  were  left  on  the  plant? 


THE   NUMBER   NINE.  161 

Alfred  had  four  nuts,  and  gave  me  two-fourths  of  what 
he  had ;  how  many  nuts  did  he  give  me  ? 

James  had  four  apples,  and  gave  his  brother  two-fourths 
of  what  he  had  ;  how  many  apples  did  he  give  his  brother  ? 

Charley  had  four  fish-hooks,  and  traded  away  two- 
fourths  of  them  ;  how  many  did  he  trade  away  ? 

Fred  caught  four  fish,  but  three-fourths  of  them  were 
too  small  to  eat,  so  he  put  them  back  in  the  water ;  how 
many  did  he  put  back  ? 

A  fisherman  had  four  boats ;  three-fourths  of  the  num- 
ber he  had  leaked  ;  how  many  leaked  ? 

In  a  class  there  were  eight  children  ;  one-fourth  of  the 
number  was  absent;  how  many  fourths  were  at  school? 

If  two-fourths  had  been  absent,  how  many  children 
would  have  been  absent? 

If  three-fourths  of  the  children  were  at  school,  how 
many  were  at  school  ? 

If  you  have  five  buttons  on  your  boot,  and  mamma  sews 
three  more  on  your  boot,  how  many  buttons  will  there  be 
on  your  boot  ? 

If  there  are  five  little  girls  on  one  side  of  the  table,  and 
three  boys  on  the  opposite  side  of  the  table,  how  many 
children  are  there  about  the  table? 

Mary  had  four  two-cents  pieces,  and  spent  three  cents ; 
how  many  cents  had  she  left  ? 

If  she  had  spent  five  cents,  how  many  cents  would  she 
have  had  remaining  ? 

In  the  barn  are  four  spans  of  horses.  If  a  span  of  horses 
and  a  single  horse  are  taken  out  of  the  barn,  how  many 
horses  will  remain  in  the  barn  ? 

If  two  spans  and  ^  single  horse  are  taken  out,  how 
many  horses  will  be  left  in  the  barn  ? 

I  have  enough  berries  to  fill  four  two-quart  measures. 
If  I  sell  three  quarts,  how  many  quarts  shall  I  have  left? 


162  riRST   STEPS    IN   NUMBER. 

If  I  sell  five  quarts,  how  many  quarts  shall  I  have  left? 

Two  chairs  were  stored  away  in  the  attic ;  one  chair  had 
lost  two  legs,  and  the  other  chair  one  leg ;  how  many  legs 
did  both  chairs  have  together  ? 

If  one  chair  had  lost  three  legs,  and  the  other  chair  two 
legs,  how  many  legs  would  the  two  chairs  have  ? 

Three  oranges  and  how  many  oranges  are  eight  oranges  ? 

Five  oranges  and  how  many  oranges  are  eight  oranges  ? 

Eight  oranges  minus  how  many  oranges  are  five  oranges? 

Eight  oranges  minus  how  many  oranges  are  three  oranges? 

Draw  a  line  an  inch  long  on  the  board.  Measure  off  on 
the  edge  of  the  table  what  you  think  to  be  an  inch. 

Divide  this  strip  of  paper  into  inches. 

Mark  off  this  line  into  inches. 

Tell  me  how  long  you  think  the  side  of  this  square  is ; 
the  side  of  this  triangle  ;  the  longer  side  of  this  oblong  ;  the 
shorter  side  of  the  oblong. 

Divide  this  figure  on  the  board  into  inch  squares. 

How  many  inches  high  is  this  gill  measure  ?  How  many 
inches  across  the  bottom  ? 

How  many  times  must  you  fill  the  gill  measure  to  dip 
out  a  pint  of  water  ? 

If  it  takes  a  gill  of  molasses  for  one  pot  of  baked  beans, 
how  many  pints  of  molasses  will  be  required  for  four  pots 
of  baked  beans  ? 

If  it  takes  a  pint  of  milk  for  a  custard,  how  many  gills 
of  milk  does  it  take  ? 

If  it  takes  a  pint  of  berries  for  a  pudding,  how  many 
times  must  Harry  fill  his  gill  cup  to  have  enough  berries 
for  the  pudding  ? 

A  pint  of  ice  cream  will  furnish  how  many  persons  a  gill 
each? 

We  have  two  pints  of  milk  every  morning.  How  many 
gills  do  we  have  ?     How  many  quarts  of  milk  do  we  have  ? 


THE   NUMBER   NINE.  163 

A  coffee-cup  holds  two  gills ;  how  many  cupfulls  will  it 
take  to  fill  a  pint  measure?  How  many  will  it  take  to 
fill  two  pint  measures  ?  How  many  will  it  take  to  fill  a 
quart  measure  ? 

I  picked  eight  pints  of  cranberries ;  how  many  quarts 
of  cranberries  did  I  pick  ? 

There  are  eight  pints  of  cream  in  the  cream-pail ;  how 
many  quarts  of  cream  are  in  the  pail  ? 

Large  milk-cans  hold  eight  quarts  of  milk.  If  the  milk- 
can  is  half  full,  how  many  quarts  are  in  the  can  ?  How 
many  pints  ? 

If  I  had  eight  pans  of  milk  to  skim,  and  I  have  skimmed 
half  of  them,  how  many  have  I  skimmed  ? 

The  snow  is  two  feet  deep  now,  which  is  half  as  deep 
as  it  has  been  ;  how  deep  has  it  been  ? 

There  are  four  links  in  half  an  inch  of  my  watch-chain ; 
how  many  links  are  there  in  an  inch  of  my  watch-chain  ? 

There  are  eight  apples  in  the  fruit-dish ;  to  how  many 
boys  can  I  give  two  apples  apiece  ? 

• 
Seven  and  Two. 

Here  are  seven  dolls.  Put  two  more  dolls  with  them^; 
how  many  dolls  are  there  now  ? 

You  may  tell  me  about  seven  blocks  and  two  blocks ; 
seven  dots  on  one  half  of  the  card  and  two  on  the  other 
half ;  seven  splints  and  two  splints ;  seven  straight  lines 
and  two  curved  lines ;  seven  horses  and  a  span  of  horses ; 
seven  butterflies  and  two  butterflies ;  seven  girls  and  two 
boys  ;  seven  chimneys  and  two  chimneys  ;  seven  robins  and 
two  bobolinks ;  seven  cows  and  a  pair  of  oxen. 

Fannie  found  seven  ripe  strawberries  in  the  morning, 
and  two  in  the  afternoon ;  how  many  ripe  strawberries  did 
she  find  in  all  ? 


164  FIRST  STEPS   IN   NUMBER. 

Near  a  thistle  are  seven  *yellow  butterflies.  If  two 
more  yellow  butterflies  come,  how  many  yellow  butterflies 
will  there  be  ? 

Seven  loads  of  hay  passed  my  house  yesterday  and  two 
to-day.  How  many  loads  of  hay  passed  yesterday,  and 
to-day  ? 

There  was  a  shower  every  day  last  week,  and  there  have 
been  two  showers  this  week.  How  many  showers  have  we 
had  within  two  weeks  ? 

I  stayed  a  week  and  two  days  at  the  beach  last  summer. 
How  many  days  did  I  stay  at  the  beach  ? 

I  can  see  from  my  window  two  beech-trees,  five  maple- 
trees,  and  two  elms.     How  many  trees  can  I  see  ? 

There  are  four  ducks  in  the  pond,  three  on  the  bank,  and 
two  more  coming.     How  many  ducks  are  there  in  all  ? 

I  have  two  nuts,  Mary  has  twice  as  many  and  one  more, 
and  Jennie  has  two.     How  many  nuts  have  we  together  ? 

If  Frank  has  one  cent,  Harry  six  times  as  many  cents, 
and  Ellen  two  cents,  how  many  cents  have  the  three 
together  ? 

If  John  has  five  cents  and  spends  three  cents,  then  earns 
five  cents,  and  I  give  him  two  cents,  how  many  cents  will 
he  have  ? 

Write  :  Seven  and  two  are  nine. 

Two   and   Seven. 

Take  nine  blocks.  Separate  them  as  I  do  mine.  How 
many  here?  (Two.)  How  many  here?  (Seven.)  Show 
me  two  of  your  blocks.  Show  me  seven  of  your  blocks. 
How  many  blocks  are  your  two  blocks  and  your  seven 
blocks? 

Here  are  two  lines  on  the  board ;  draw  enough  more  to 
make  nine  lines.     How  many  did  you  draw  ? 


THE   NUMBER   NINE.  165 

Here  are  two  dots.  Make  enough  more  dots  to  have 
nine  dots.     How  many  did  you  make  ? 

In  a  basket  of  fruit  were  two  pears  and  seven  apples. 
How  many  pears  and  apples  were  there  together  ? 

The  tickets  to  a  concert  are  a  half-dollar  each.  If  I  take 
two  tickets,  and  the  rest  of  the  family  take  seven  tickets, 
how  many  half-dollars  do  we  pay  for  tickets  to  the  concert  ? 
How  many  dollars  ? 

I  have  two  quarters  of  a  dollar  in  my  purse  and  enough 
change  to  make  seven  quarters  more.  How  much  money 
have  I  in  my  purse  ? 

One  side  of  this  right  angle  is  two  inches  long,  and  the 
other  side  is  seven  inches  long.  How  long  are  both  sides 
of  the  angle  ? 

Two  honey-bees  were  on  a  morning-glory,  and  seven 
others  were  flying  near.  How  many  honey-bees  were  there 
in  all? 

There  are  two  black  spools  on  this  string,  and  seven  white 
spools.     How  many  spools  are  on  the  string  ? 

Edward  has  two  cents.  Mary  has  three  times  as  many 
cents  and  one  cent  beside.  How  many  cents  have  they 
together  ? 

Charlie  has  a  two-cent  piece  of  money.  I  have  two 
three-cent  pieces  of  money  and  one  cent  beside.  How 
much  money  have  we  together  ? 

You  may  tell  me  a  story  about  two  and  seven. 

Write  :  Two.  and  seven  are  nine. 

Nine  minus  Two. 

I  have  nine  dots  on  the  board ;  I  will  cover  two.  How 
many  can  you  see  now  ? 

Here  are  nine  tin  plates ;  I  will  bake  pies  on  two  of  the 
plates.     How  many  plates  will  be  left  in  the  pile  ? 


166  FIRST  STEPS   IN   NUMBER. 

Here  are  nine  paper  wheels ;  play  they  are  water-wheels 
and  that  you  have  set  two  of  them  in  the  brook.  How 
many  will  you  have  left  ? 

Pick  out  nine  birds  from  the  box  of  patterns ;  play  two 
flew  away.     How  many  are  left  ? 

Find  nine  horses.  Hitch  a  span  to  a  cart.  How  many 
horses  have  you  beside  the  span  ? 

Nine  tops  were  spinning  at  the  same  time.  Two  tumbled 
over.     How  many  were  then  spinning  ? 

There  were  nine  chickens  in  a  brood.  Two  were  white 
and  the  rest  were  brown.     How  many  were  brown  ? 

There  were  nine  panes  of  glass  in  the  lower  sash  of  a 
window.  One  pane  was  broken  and  another  cracked. 
How  many  were  whole  ? 

I  had  nine  postal  cards  this  morning,  but  I  have  used 
two.     How  many  have  I  left? 

Nine  boys  were  playing  ball,  but  two  left  the  game. 
How  many  remained  playing. 

There  were  nine  things  in  my  pencil  tray ;  I  took  out  a 
pencil  and  an  eraser.  How  many  things  remained  in  the 
tray? 

Each  think  of  a  story  for  nine  minus  two.  Who  has  a 
story  ready  ?     Tell  me  your  story. 

Write  :  Nine  minus  two  are  seven. 


Nine  minus  Seven. 


Show  me  nine  cubical  blocks ;  put  back  seven.  How 
many  remain? 

Show  me  nine  rectangular  blocks  ;  put  back  seven.  How 
many  remain? 

Show  me  nine  lines  on  the  board ;  erase  seven.  How 
many  lines  remain  ? 


THE   NUMBER   NINE.  157 

Here  are  nine  soldier  caps.  Seven  soldiers  have  taken 
their  caps.     How  many  caps  are  left? 

There  are  nine  cars  on  a  passenger  train ;  one  car  was  a 
smoking  car,  two  cars  were  sleepers,  and  four  cars  were 
ordinary  passenger  cars;  the  rest  were  baggage  cars. 
How  many  were  baggage  cars  ? 

There  were  nine  books  on  a  shelf;  four  had  red  backs, 
three  had  green  backs,  and  the  rest  were  brown.  How 
many  were  brown  ? 

Nine  bottles  stood  on  a  shelf;  two  had  glycerine  in 
them,  five  had  medicine,  and  the  rest  were  empty.  How 
many  were  empty  ? 

There  are  nine  more  days  in  this  month  ;  how  many  days 
will  there  be  after  a  week  has  passed  ? 

A  boy  had  nine  cents ;  he  spent  two  cents  each  day  for 
three  days  and  one  cent  the  next  day.  How  many  cents 
had  he  then  ? 

If  he  had  spent  three  cents  each  day  for  two  days  and 
one  cent  beside,  how  many  cents  would  have  remained  ? 

If  he  had  spent  two  cents  each  day  for  two  days  and 
three  the  next  day,  how  many  cents  would  have  remained  ? 

If  he  had  spent  a  cent  each  day  for  five  days  and  two 
beside,  how  many  cents  would  have  remained  ? 

Tell  me  about  nine  minus  seven. 

Write :  Nine  minus  seven  are  two. 


Exercise  for  Review. 

Five  and  two  and  how  many  are  nine  ? 
Four  and  three  and  how  many  are  nine  ? 
One  and  six  and  how  many  are  nine  ? 
Four  and  four  and  how  many  are  nine  ? 
Five  and  three  and  how  many  are  nine  ? 


168  FIRST  STEPS   IN  NUMBER. 

Two  and  six  and  how  many  are  nine  ? 

One  and  three  and  two  and  two  and  how  many  are 
nine  ? 

Two  and  three  and  two  and  how  many  are  nine  ? 

There  were  nine  apples  in  a  dish ;  two  were  sweet  and 
the  rest  were  sour.     How  many  were  sour  ? 

Charlie  had  nine  pencils ;  three  were  too  short  to  use, 
and  four  were  not  sharpened ;  how  many  were  ready  for  use  ? 

Nine  minus  what  number  is  eight  ? 

Nine  minus  what  number  is  seven? 

Nine  minus  what  number  is  one  ? 

Nine  minus  what  number  is  two  ? 

Tell  me  two  numbers  you  may  take  from  nine  and  have 
two  remain. 

What  two  equal  numbers  make  eight  ? 

What  two  equal  numbers  make  six  ? 

What  two  equal  numbers  make  four  ? 

What  two  numbers,  one  of  which  is  one  more  than  the 
other,  make  five? 

What  two  numbers,  one  of  which  is  one  more  than  the 
other,  make  three  ? 

What  two  numbers,  one  of  which  is  one  more  than  the 
other,  make  seven? 

What  two  numbers,  one  of  which  is  two  more  than  the 
other,  make  eight  ? 

How  many  pairs  of  gloves  have  I  if  I  have  eight  single 
gloves  ? 

I  have  two  cents;  James  has  twice  as  many.  How 
much  money  have  we  together  ? 

Nellie  has  two  dolls;  Ida  has  four  times  as  many. 
How  many  more  dolls  has  Ida  than  Nellie  ? 

Old  Dolly  can  travel  two  miles  in  half  an  hour ;  the 
colt  can  travel  twice  as  fast.  How  far  will  the  colt  travel 
in  an  hour  ? 


THE   NUMBER   NINE.  169 

Apples  are  selling,  two  for  a  cent,  but  if  you  buy  a 
single  apple  you  must  pay  a  cent.  How  much  will  nine 
apples  cost? 

Lemons  are  selling,  two  for  three  cents.  How  many 
lemons  can  you  buy  for  six  cents  ? 

If  an  orange  were  divided  equally  between  two  boys, 
what  part  of  the  orange  would  each  boy  have  ? 

If  two  oranges  were  divided  equally  between  two  boys, 
what  part  of  the  two  oranges  would  each  boy  have  ?  How 
many  oranges  would  each  have  ? 

If  four  oranges  were  divided  equally  between  two  boys, 
what  part  of  the  four  oranges  would  each  boy  have  ?  How 
many  oranges  would  each  have  ? 

Two  is  half  of  what  number  ? 

Four  is  half  of  what  number  ? 

One  is  half  of  what  number  ? 

Three  is  half  of  what  number  ? 

If  an  orange  were  divided  equally  among  four  boys, 
what  part  of  the  orange  would  each  boy  have  ? 

If  four  oranges  were  divided  equally  among  four  boys, 
what  part  of  the  four  oranges  would  each  boy  have  ?  How 
many  oranges  would  each  boy  have  ? 

If  eight  oranges  were  divided  equally  among  four  boys, 
what  part  of  the  eight  oranges  would  each  boy  have  ?  How 
many  oranges  would  each  boy  have  ? 

One  is  one-fourth  of  what  number  ? 

Two  is  one-fourth  of  w^hat  number  ? 

Jamie  has  two  two-cent  pieces  of  money  and  three  cents. 
How  much  money  must  he  earn  to  have  nine  cents? 

A  boy  had  nine  clothes-brooms  to  sell.  When  he  had 
sold  all  but  two,  how  many  had  he  sold  ? 

If  you  bought  two  papers  of  needles  for  six  cents,  and 
gave  in  payment  a  five-cent  piece  and  a  three-cent  piece, 
how  much  change  should  you  receive  ? 


170  FIRST  STEPS   IN   NUMBER. 

For  eight  cents,  how  many  plums  at  three  cents  each 
can  you  buy,  and  how  many  cents  will  you  have  toward 
buying  another  plum  ? 

For  seven  cents,  how  many  tops  at  four  cents  each  can 
I  buy.  and  how  many  cents  will  be  left  ? 

Six  and  Three. 

Show  me  six  blocks.  Now  show  me  half  as  many  more. 
How  many  have  you  shown  me  in  all  ? 

Show  me  six  buttons ;  put  with  them  half  as  many  but- 
tons as  you  have  shown  me.  How  many  buttons  have  you 
now? 

In  one  keg  were  six  gallons  of  maple  syrup,  and  in 
another  three  gallons.  How  many  gallons  were  in  both 
kegs? 

If  the  postage  on  a  package  was  six  cents,  and  the  postage 
on  a  letter  three  cents,  how  much  was  the  postage  for  both  ? 

Three  boys  started  fishing ;  they  met  three  other  boys 
who  went  with  them.  If  three  more  had  gone  with  them, 
how  many  would  have  gone  fishing  ? 

James  earned  two  cents  one  day,  twice  as  much  the  next 
day,  and  three  cents  the  next  day.  How  many  cents  did 
he  earn  in  all  ? 

I  have  a  five-cent  piece,  one  cent,  and  a  three-cent  piece. 
How  much  money  have  I  ? 

I  have  a  pitcher  which  holds  a  pint  and  a  half  and  three 
gills  more.     How  many  gills  does  the  pitcher  hold  ? 

If  I  work  six  hours  during  the  day,  and  three  hours  in 
the  evening,  how  many  hours  do  I  work  in  all  ? 

I  can  see  four  doves,  two  blue-birds,  and  three  robins. 
How  many  birds  can  I  see  ? 

Tell  me  a  story  about  six  and  three.  Another ;  another  ; 
another. 

Write :  Six  and  three  are  nine. 


THE   NUMBER   NINE.   ^',  171 


Three  and  Six. 


Show  me  three  pencils ;  put.  with  them  twice  as  many 
pencils.  How  many  pencils  have  yon  ?  Show  me  this 
with  lines  on  the  board ;  with  dots  on  the  board ;  with 
splints  at  the  table ;  with  squares  of  paper. 

If  I  tell  you  three  stories  about  three  and  six,  and  you 
tell  me  twice  as  many  stories,  how  many  stories  shall  we 
both  tell  ? 

If  there  were  three  boys  on  one  sled,  and  twice  as  many  on 
another  sled,  how  many  boys  were  on  both  sleds  together  ? 

If  there  were  three  milk-cans  right  side  up  on  the  bench, 
and  twice  as  many  turned  down,  how  many  milk-cans  were 
there  on  the  bench  ? 

If  I  walk  three  miles  in  this  direction,  and  you  travel 
twice  as  far  in  the  opposite  direction,  how  far  apart  shall 
we  be? 

If  a  pen  and  pen-holder  cost  three  cents,  and  a  bottle 
of  ink  cost  six  cents,  how  much  do  both  cost  ? 

If  you  have  three  half-dollars  and  I  have  six  half-dollars, 
how  many  half-dollars  have  we  both  together? 

Tell  me  about  three  hens  and  six  hens ;  about  three 
lamps  and  six  lamps ;  about  three  flags  and  six  flags ; 
about  three  combs  and  six  combs;  about  three  saws  and 
six  saws ;  about  three  horses  and  six  cows ;  about  three 
robins  and  six  swallows  ;  about  three  lanibs  and  six  sheep ; 
about  three  knives  and  six  spoons. 

Write :  Three  and  six  are  nine. 

Nine  minus  Three. 

Show  me  nine  fingers  ;  shut  down  three.  How  many 
fingers  do  you  now  show  me  ? 


172  FIRST  STEPS   IN   NUMBER. 

Here  are  nine  cents ;  give  me  three  of  them.  How  many 
cents  are  left  ? 

Here  are  nine  dots  arranged  in  several  ways  on  the 
board.  Erase  three  in  each  case  and  see  how  many 
remain. 

Nine  ducks  were  in  the  pond,  but  three  went  out  on 
the  bank.     How  many  ducks  were  then  in  the  pond  ? 

There  are  nine  dots  on  the  card  I  have  here.  Three 
dots  are  on  one  half,  how  many  dots  are  on  the  other 
half? 

The  school-bell  rings  nine  times  during  the  day.  If  it 
rings  three  times  in  the  afternoon,  how  many  times  does 
it  ring  in  the  morning  ? 

I  had  nine  cents  and  bought  a  three-cent  postage-stamp ; 
how  many  cents  had  T  left  ? 

There  were  nine  doves  on  the  walk,  but  three  flew  up  on 
the  roof.     How  many  remained  on  the  walk  ? 

I  had  nine  callers  to-day ;  three  came  in  the  morning, 
and  the  others  in  the  afternoon.  How  many  came  in  the 
afternoon  ? 

A  hen  had  nine  chickenp,  but  a  weasel  caught  three  of 
them.     How  many  were  left  ? 

A  boy  who  had  nine  cookies  ate  three.  To  how  many 
boys  could  he  give  the  rest  of  his  cookies  if  he  gave  two  to 
each  boy  ? 

Alice  found  nine  pins ;  three  were  bent,  and  half  of  the 
rest  had  no  points.     How  many  were  good  to  use  ? 

Gertie  had  nine  gold  beads.  She  gave  three  of  them 
away,  lost  half  of  the  rest,  and  afterwards  lost  two  more ; 
how  many  beads  did  she  have  left  ? 

Nettie  had  nine  Easter  eggs.  She  kept  three  herself  and 
divided  the  rest  between  her  sisters,  giving  them  three 
apiece.     How  many  sisters  had  she  ? 

Nellie  spent  nine  days  in  the  city  ;  three  days  were  rainy, 


THE   NUMBER   NINE.  173 

and  she  stayed  in  the  house ;  half  of  the  other  days  and 
one  more  day  she  rode  and  walked  about  the  city.     How 
many  more  days  had  she  to  stay  in  the  city  ? 
Write  :  Nine  minus  three  are  six. 


Nine  minus  Six. 

Here  are  nine  lines.  Cover  six  with  your  hand  and  tell 
me  how  many  you  can  see. 

Make  nine  zq  on  the  board.  After  you  had  made  six, 
how  many  more  had  you  to  make  ? 

Here  are  nine  nuts.  Give  six  to  Mary.  How  many 
have  you  ? 

Of  nine  chairs  in  our  dining-room,  only  six  have  cane 
seats.     How  many  have  not  cane  seats? 

There  are  nine  pencils  on  my  desk.  Three  are  not  sharp- 
ened, and  three  are  too  short  to  use.  How  many  are  fit 
for  use  ? 

I  spent  nine  cents  this  morning.  I  bought  three  papers 
of  needles  at  two  cents  a  paper,  and  spent  the  rest  for  hat- 
pins at  a  cent  a  pin.     How  many  pins  did  I  buy  ? 

I  have  nine  pet  mice.  Three  are  white,  three  are  brown, 
and  the  rest  are  black.     How  many  are  black  ? 

John  has  nine  glass  marbles.  Two  are  striped  with  red, 
four  are  green,  and  the  rest  are  purple.  How  many  are 
purple. 

Here  are  nine  cents.  Two  cents  belong  to  Fred,  twice 
as  many  to  George,  and  the  rest  to  me.  How  many  cents 
belong  to  me  ? 

Here  are  nine  blocks.  If  you  put  one  block  in  a  pile  by 
itself,  two  blocks  in  another  pile,  and  three  in  another,  how 
many  blocks  will  remain  for  the  fourth  pile  ? 

Tell  me  a  story  for  nine  minus  six.     Another ;  another. 

Write  :  Nine  minus  six  are  three. 


174  FIRST   STEPS    IN   NUMBER. 

Nine  divided  by  Three. 

Pick  out  nine  blocks.  Put  them  in  piles  of  three  each. 
How  manj  piles  have  you  ? 

Take  nine  cups.  Pile  them  up,  three  in  each  pile,  and 
see  how  many  piles  you  have. 

Distribute  these  nine  pencils,  giving  three  to  each  child. 
To  how  many  children  have  you  given  them  ? 

Here  are  nine  cents.^  To  how  many  three-cent  pieces 
are  they  equal  ? 

How  many  three-cent  stamps  can  I  buy  for  nine  cents? 
How  many  three-cent  pencils?  How  many  three-cent 
books  ?  How  many  three-cent  cards  ?  How  many  three- 
cent  spools  of  cotton  ? 

If  a  newspaper  is  sold  for  three  cents,  and  the  newsboy 
has  taken  nine  cents,  how  many  papers  has  he  sold  ? 

When  blueberries  are  three  cents  a  pint,  how  many 
pints  can  I  buy  for  nine  cents  ? 

How  many  pints  of  milk  can  I  buy  for  nine  cents,  when 
milk  is  three  cents  a  pint  ? 

If  an  apple  costs  one  cent,  and  a  pear  two  cents,  how 
many  apples  and  pears  can  I  buy  for  nine  cents  ? 

If  an  orange  costs  two  cents,  and  a  stick  of  taffy  one  cent, 
how  many  oranges  and  sticks  of  taffy  can  I  buy  for  nine 
cents  ? 

If  a  pen  costs  one  cent,  a  pencil  one  cent,  and  a  star- 
book  one  cent,  how  many  pens,  pencils,  and  star-books  can 
I  buy  for  nine  cents? 

At  each  board  there  are  three  crayons.  How  many 
boards  will  nine  crayons  supply  ? 

If  Eddie  earns  three  cents  a  day,  how  many  days  must 
he  work  to  earn  nine  cents  ? 

I  have  nine  pieces  of  apple  here.  If  three  of  them  will 
make  a  whole  apple,  how  many  whole  apples  have  I  ? 


THE  NUMBER  NINE.  175 

I  liave  nine  finger  rings.  If  I  should  wear  three  on  each 
finger,  on  how  many  fingers  should  I  wear  them  ? 

In  a  barge  three  persons  can  sit  on  a  seat ;  how  many 
seats  must  the  barge  contain  for  nine  persons  ? 

You  may  tell  me  a  story  about  the  number  of  threes  in 
nine. 

Write :  There  are  three  threes  in  nine. 

Three  Threes. 

Show  me  three  squares  on  the  board  with  three  dots  in 
each  square.     How  many  dots  do  you  show  me  ? 

Show  me  three  triangles  with  a  dot  in  each  corner.  How 
many  dots  do  you  show  me? 

How  many  corners  have  three  triangles  ? 

How  many  sides  have  three  triangles  ? 

On  each  of  these  three  plates  are  three  buttons  which  we 
will  call  apples.     How  many  apples  are  on  all  the  plates  ? 

Show  me  three  piles  of  blocks  with  three  in  a  pile.  How 
many  blocks  do  you  show  me  ? 

Show  me  three  boxes  with  three  splints  in  each  box. 
How  many  splints  do  you  show  me  ? 

Call  your  splints  spoons,  and  show  me  three  cups  with 
three  spoons  in  each  cup.  How  many  spoons  do  you  show 
me? 

If  there  are  three  birds'  nests  with  three  eggs  in  each 
nest,  how  many  eggs  are  in  all  the  nests  ? 

In  each  of  these  boxes  are  three  dozen  crayons.  How 
many  dozen  crayons  are  there  in  three  boxes  ? 

If  I  have  three  cents,  and  Alice  has  three  times  as  many 
cents,  how  many  cents  has  Alice  ? 

In  one  can  are  three  pints  of  milk,  and  in  another  are 
three  times  as  much  milk.  How  many  pints  of  milk  in 
the  other  can  ? 


176  FIRST   STEPS   IN   NUMBER. 

Mabel  learns  three  new  words  a  day.  If  Willie  learns 
three  times  as  many  words,  how  many  words  does  Willie 
learn  ? 

I  can  walk  three  miles  an  hour.  How  far  can  I  walk  in 
three  hours  ? 

Here  are  three  blocks  in  this  row.  In  the  longer  row 
are  three  times  as  many  blocks.  How  many  blocks  are  in 
the  longer  row  ? 

This  line  is  three  inches  long.  The  line  above  it  is  three 
times  as  long.     How  long  is  the  longer  line  ? 

One  pail  holds  three  pints.  Another  pail  holds  three 
times  as  much.  How  many  quarts  does  the  larger  pail 
hold? 

One  pitcher  contains  three  gills.  Another  contains  three 
times  as  many  gills.  How  many  pints  does  the  larger 
pitcher  hold  ? 

Tell  me  a  story  for  three  threes  are  nine. 

Write  :  Three  threes  are  nine. 


Exercise  for  Revie^v. 

If  a  bunch  of  envelopes  costs  six  cents,  and  a  stamp  three 
cents,  how  much  do  both  cost  ? 

A  fly  has  six  legs.  If  he  had  three  more  legs,  how  many 
legs  would  he  have  ? 

Two  lilies,  four  pansies,  and  three  geranium  blossoms  are 
how  many  blossoms  ? 

There  were  nine  spoons  in  the  spoon-holder,  but  I  have 
taken  out  three.     How  many  remain  in  the  spoon-holder  ? 

Nine  ants  were  carrying  ofl"  a  big  bug,  but  three  of  them 
left  off  to  rest.  How  many  were  then  carrying  away  the 
bug? 

Nine  flies  were  in  the  spider's  web  this  morning,  but  he 
has  eaten  three.     How  many  are  left  in  the  web  ? 


THE   NUMBER   NINE.  177 

I  bought  six  pencils,  used  four,  then  bought  seven  more, 
and  used  three.     How  many  pencils  did  I  then  have  ? 

In  the  barn  are  three  swallows'  nests.  If  six  more  are 
built,  how  many  swallows'  nests  will  there  be  ? 

In  my  work-basket  are  three  spools  of  white  thread,  and 
six  spools  of  dark  thread.  How  many  spools  of  thread  are 
in  my  work-basket  ? 

If  I  should  use  two  spools  of  white  thread,  and  four 
spools  of  dark  thread,  how  many  spools  would  remain  ? 

In  a  basket  are  nine  eggs.  If  I  use  half  a  dozen  eggs, 
how  many  eggs  will  there  be  in  the  basket  ? 

If  a  pail  holds  nine  pints  of  water,  and  there  is  in  the 
pail  a  quart  and  a  half  of  water,  how  many  more  pints  will 
the  pail  hold? 

Six  and  how  many  are  nine  ? 

Three  and  how  many  are  nine  ? 

Nine  minus  six  are  how  many  ? 

Nine  minus  three  are  how  many? 

Nine  minus  what  number  leaves  three  ? 

Nine  minus  what  number  leaves  six  ? 

Three  girls  going  berrying  have  each  a  three-pint  pail. 
If  each  gets  her  pail  full,  how  many  pints  of  berries  will 
they  bring  home  ?  How  many  quarts  of  berries  and  what 
part  of  a  quart  beside  ? 

If  one  whistle  costs  three  cents,  what  will  three  whistles 
cost? 

Which  will  hold  the  more,  three  three-pint  pails,  or  a 
four-quart  pail?  Two  three-pint  pails,  or  a  three-quart  pail? 
A  three-pint  pail,  or  a  two-quart  pail  ?  A  quart  measure, 
or  a  pitcher  that  holds  eight  gills. 

Which  will  measure  the  more,  two  pieces  of  lace  each 
three  inches  long,  or  three  pieces  of  lace  each  two  inches 
long  ?  Four  strips  of  braid  each  two  inches  long,  or  two 
strips  of  braid  each  four  inches  long  ? 


178  FIRST  STEPS   IN   NUMBER. 

If  this  square  box  is  two  inches  on  each  side,  how  many 
inches  is  it  around  the  box  ? 

If  the  two  longer  sides  of  this  box  are  each  two  inches 
long,  and  the  shorter  sides  each  an  inch,  how  far  is  it  around 
this  box  ? 

It  is  two  miles  to  the  post-office,  and  three  times  as  far 
from  the  post-office  to  the  depot.  How  far  is  it  to  the 
depot? 

There  is  nothing  in  this  box.  How  much  will  there  be 
in  nine  such  boxes? 

If  two  apples  cost  a  cent,  how  much  will  four  apples 
cost  ?  six  apples  ?  eight  apples  ? 

If  you  and  I  have  each  four  apples,  but  two  of  mine  are 
not  good,  how  many  of  yours  must  you  give  me  that  I  may 
have  just  as  many  good  apples  as  you  have  left? 

What  two  numbers,  one  of  which  is  twice  as  large  as  the 
other,  make  nine? 

I  will  give  a  number,  and  you  may  give  me  the  number 
which  put  with  mine  will  make  nine  :  two  ;  seven  ;  three ; 
six  ;  one  ;  eight. 

Give  me  a  number  which  put  with  the  number  I  give 
you  will  make  eight :  one  ;  two  ;  four  ;  six  ;  three  ;  five  ; 
seven  ;  eight. 

Nellie  bought  three  lemons,  at  three  cents  apiece.  She 
gave  three  pieces  of  money  in  payment.  What  were  the 
pieces  of  money  ? 

Harry  had  nine  cents,  and  spent  three  cents ;  Fred  had 
four  cents,  and  earned  four  more  cents.  How  much  more 
money  had  Fred,  at  last,  than  Harry? 

If  I  have  eight  cents,  and  spend  a  cent  a  day,  and  you 
have  none,  but  earn  a  cent  a  day,  in  how  many  days  shall 
we  have  the  same  amount  ? 

What  three  different  numbers  added  together  make 
six? 


THE   NUMBER   NINE.  179 

From  what  number  can  you  subtract  half  of  itself  and 
leave  two  ?  leave  three  ?  leave  four  ? 

Two  halves  of  an  apple  are  how  many  apples  ? 
Two  halves  of  two  apples  are  how  many  apples  ? 
Two  halves  of  four  apples  are  how  many  apples  ? 
Two  halves  of  six  apples  are  how  many  apples  ? 

Five  and  Four. 

Take  nine  blocks.  Separate  them  into  two  groups,  one 
of  which  groups  shall  contain  one  more  block  than  the 
other.  How  many  in  the  larger  group  ?  How  many  in 
the  smaller  group  ?  Five  blocks  and  four  blocks  are  how 
many  blocks  ? 

Show  me  five  splints,  and  four  splints.  How  many 
splints  do  you  show  me  ? 

Show  me  five  fingers  on  one  hand,  and  four  on  the  other 
hand.     How  many  fingers  do  you  show  me  ? 

Find  five  red  squares,  and  four  blue  squares.  How 
many  squares  have  you  found  ? 

There  are  five  dots  on  one  half  of  this  card,  and  four  dots 
on  the  other  half.     How  many  dots  are  on  the  card  ? 

In  one  hand  I  have  five  yellow  disks ;  in  the  other  hand 
I  have  one  less  than  fi\e  disks.  How  many  disks  have  I 
in  both  hands  ? 

Here  is  a  three-cent  coin,  a  two-cent  coin,  and  four  cents. 
How  many  cents  are  they  worth  ? 

Alice  bought  five  lead  pencils  for  a  cent  apiece,  and  four 
slate  pencils  at  a  cent  apiece.    How  much  did  the  pencils  cost  ? 

James  bought  a  book  for  three  cents,  a  pop-gun  for  two 
cents,  and  two  candy  mice  at  two  cents  apiece.  How  many 
cents  did  he  spend  ? 

Addie  made  seven  Z's  on  her  slate,  erased  two,  and  then 
made  four  more.     How  many  Z's  were  then  on  her  slate  ? 


180  FIRST  STEPS   IN   NUMBER. 

A  train  of  cars  ran  eight  miles,  then  backed  three  miles, 
then  went  ahead  four  miles  to  the  next  station.  How  far 
was  it  between  the  stations  ? 

One  boat  went  up  the  river  five  miles,  and  another  boat 
went  down  the  river  four  miles.  If  the  boats  started  from 
the  same  point,  how  far  apart  were  they  then  ? 

Who  thinks  of  a  story  about  five  and  four  ? 

Mary?  Alice?  Annie?  Susie?  Ned?  John? 

Write :  Five  and  four  are  nine. 

Four  and  Five. 

Four  squirrels  lived  in  the  hollow  of  a  tree,  and  five 
more  squirrels  had  their  nests  in  the  ground,  not  far  from 
the  tree.    How  many  squirrels  lived  quite  near  each  other? 

A  man  planted  four  acres  of  corn,  and  five  acres  of  pota- 
toes.    How  many  acres  did  he  plant  ? 

In  the  youngest  class  there  are  four  girls  and  five  boys. 
How  many  children  are  in  the  class  ? 

Four  doves  were  on  the  sidewalk,  and  five  more  alighted 
on  the  sidewalk.  How  many  doves  were  then  on  the  side- 
walk? 

Four  lamps  are  in  one  row,  and  five  lamps  in  another. 
How  many  lamps  are  in  both  rows  ? 

A  pint  cup  holds  four  gills.  If  a  pitcher  holds  one  gill 
more  than  the  pint  cup,  how  many  gills  will  both  hold  ? 

Here  are  two  two-cent  coins  and  a  five-cent  coin.  To 
how  many  cents  are  they  equal  ? 

Nellie  has  found  four  four-leaved  clovers ;  Mary  has 
found  as  many,  and  one  more.  How  many  four-leaved 
clovers  have  they  found  together? 

There  are  four  crocus  blossoms  in  my  garden,  and  one 
more  than  as  many  tulip  blossoms.  How  many  blossoms  in 
all? 


THE   NUMBER   NINE.  181 

School  has  kept  two  weeks,  but  Hubert  came  only  four 
days  last  week.  How  many  days  has  Hubert  been  to 
school  this  term  ? 

How  many  cents  will  two  two-cent  stamps,  and  a  five- 
cent  stamp,  cost  ? 

Harry  and  Mary  were  hunting  for  eggs ;  Harry  found 
four,  and  Mary  found  one  more  egg  than  Harry.  How 
many  eggs  did  both  find  together? 

Some  hens  and  turkeys  are  out  by  my  window.  There 
are  four  hens,  and  one  more  turkey  than  hens.  How  many 
hens  and  turkeys  are  there,  counted  together? 

Tell  me  a  story  for  four  and  ^ve. 

Write  :  Four  and  five  are  nine. 


Nine  minus  Four. 

There  are  nine  dots  in  each  one  of  these  squares  on  the 
board.  You  may  erase  four  dots  in  one  of  the  squares. 
How  many  dots  remain  ?  Erase  four  in  another  square. 
How  many  are  left?  Erase  four  in  each  square.  How 
many  dots  are  in  each  square  now  ? 

If  there  are  nine  dots  in  a  square,  and  four  are  erased, 
how  many  dots  remain  ? 

There  are  nine  lines  on  each  of  these  boards.  Erase  four 
lines  on  each  board.     How  many  remain  on  each  board  ? 

Show  me  nine  squares  of  paper.  Put  four  squares  under 
the  table.     How  many  squares  are  left  ? 

Show  me  nine  horses.  Drive  away  two  spans.  How 
many  spans  and  what  part  of  a  span  remain  ? 

I  have  nine  gloves.  If  I  send  away  two  pairs  to  be 
cleaned,  how  many  pairs  of  gloves  are  left,  and  what  part 
of  a  pair,  beside  ? 

A  boy  who  had  nine  rabbits  sold  three  and  gave  away 
one.     How  many  did  he  then  have  ? 


182  FIRST  STEPS   IN  NUMBER. 

A  boy  playing  ninepins  knocked  four  ninepins  down  with 
the  first  ball.     How  many  ninepins  remained  standing  ? 

Nine  boys  were  playing  base-ball.  Four  of  the  boys  left 
the  game.     How  many  boys  were  left  to  play  ? 

James  earned  three  cents  a  day  for  three  days,  and 
spent  four  cents.     How  many  cents  had  he  then  ? 

There  are  three  boys  and  six  girls  in  my  middle  class. 
Four  of  the  class  have  paid  their  book-rent.  How  many 
have  not  paid  their  book-rent  ? 

Tell  me  a  story  for  nine  minus  four. 

Write:    Nine  minus  four  are  five. 


Nine  minus  Five. 

Take  nine  blocks.  Who  will  find  soonest  how  many 
blocks  remain  after  taking  five  away  ?  Tell  me  a  story  for 
this  fact.  Tell  me  a  story  for  nine  pens  minus  five  pens ; 
nine  tops  minus  five  tops ;  nine  bells  minus  five  bells ;  nine 
cups  minus  five  cups ;  nine  books  minus  five  books ;  nine 
plates  minus  five  plates ;  nine  cents  minus  five  cents ;  nine 
sheep  minus  five  sheep ;  nine  buns  minus  five  buns. 

There  are  nine  shelves  to  my  bookcase ;  five  are  wide 
and  the  others  narrow.     How  many  are  narrow  ? 

If  a  milk-can  holds  nine  quarts,  and  five  quarts  have  been 
sold,  how  many  quarts  of  milk  remain  in  the  can  ? 

Harry  peddles  newspapers.  He  has  nine  papers  left ; 
five  are  dailies,  and  the  rest  weeklies.  How  many  are 
weeklies  ? 

Ned  has  a  cent  each  day  for  carrying  the  milk.  If  he 
has  carried  the  milk  nine  days,  how  many  cents  more  than 
five  cents  ought  he  to  receive  ? 

I  have  here  a  two-cent  piece,  two  three-cent  pieces,  and  a 
cent.  If  I  give  you  a  three-cent  piece  and  a  two-cent  piece, 
how  many  cents  shall  I  have  ? 


THE   NUMBER   NINE.  183 

Henry  has  been  to  school  nine  days.  If  the  school-week 
is  five  days,  how  many  days  over  a  week  has  he  been  to 
school  ? 

I  bought  nine  cents'  worth  of  stationery  this  morning,  and 
paid  for  it  with  a  five-cent  piece  and  some  two-cent  pieces. 
How  many  two-cent  pieces  did  I  pay  ? 

Write  :    Nine  minus  five  are  four. 

Nine  minus  Nine. 

Robert  had  nine  marbles.  He  lost  five,  and  gave  away 
four.     How  many  marbles  did  he  then  have  ? 

Mary  invited  nine  little  girls  to  supper.  Two  sat  at  one 
end  of  the  table,  three  on  each  side  of  the  table,  and  one 
sat  beside  Mary  at  the  other  end  of  the  table.  How  many 
more  little  girls  were  there  to  be  seated  ? 

If  I  have  nine  cents,  and  buy  a  top  for  John  for  four 
cents,  and  some  nuts  for  Annie  for  five  cents,  how  many 
cents  have  I  left  ? 

Nellie  had  nine  paper  dolls.  She  gave  away  seven,  and 
the  dog  chewed  two.  How  many  paper  dolls  did  she  then 
have  ? 

There  were  nine  rabbits  in  the  yard,  but  when  a  dog 
ran  into  the  yard  three  ran  into  the  stable,  and  six  scam- 
pered under  the  piazza.  How  many  were  then  in  the 
yard  ? 

We  had  nine  little  chickens,  but  a  weasel  caught  two,  a 
hawk  caught  one,  three  got  drowned,  and  three  others  ate 
something  which  killed  them.  How  many  of  our  nine 
chickens  have  we  now  ? 

We  had  nine  cats  when  we  lived  on  the  farm ;  three 
were  white,  two  were  black,  four  were  gray,  and  the  rest 
yellow.     How  many  were  yellow  ? 

Nine  children  owe  me  for  their  writing-books.     If  seven 


184  FIRST  STEPS   IN   NUMBER. 

pay  me  to-day,  and  two  to-morrow,  how  many  will  still  owe 
me? 

If  a  farmer  has  only  nine  quarts  of  oats,  and  gives  his 
horse  a  quart  each  meal  for  three  days,  how  many  quarts 
will  he  have  left  ? 

If  I  have  nine  envelopes,  and  I  send  off  three  letters  one 
day,  four  letters  the  next  day,  and  two  letters  the  next  day, 
how  many  envelopes  shall  I  have  left  ? 

Tell  me  a  story  for  nine  minus  nine. 

"Write :    Nine  minus  nine  is  none. 

Nine  Ones. 

Here  are  nine  cards,  with  a  dot  on  each  card.  How 
many  dots  are  there  ? 

There  are  nine  slates  on  the  desks,  and  a  pencil  on  each 
slate.     How  many  pencils  are  there  in  all  ? 

Each  slate  pencil  cost  a  cent.  How  many  cents  did  the 
nine  slate  pencils  cost? 

How  many  cents  would  nine  sticks  of  candy  cost,  if  each 
stick  of  candy  cost  a  cent  ? 

Nine  boys  have  each  a  knife.  How  many  knives  have 
they  together  ? 

Charlie  receives  a  cent  for  every  newspaper  he  sells. 
How  many  cents  will  he  receive  for  selling  five  newspapers 
in  the  morning  and  four  newspapers  in  the  afternoon  ? 

A  man  earns  a  dollar  a  day.  If  he  works  three  days  a 
week  for  three  weeks,  how  many  dollars  will  he  earn? 

If  each  bottle  has  ^  stopple,  how  many  stopples  will  nine 
bottles  have  ? 

If  I  send  off  four  letters  a  day  for  two  days,  and  one  let- 
ter the  next  day,  how  many  envelopes  shall  I  need  for  my 
letters? 

Write :    Nine  ones  are  nine. 


THE   NUMBER   NINE.  185 

Nine  divided  by  One. 

Take  nine  buttons.  Put  one  button  into  each  box.  How 
many  boxes  does  it  take  ? 

Mary  has  nine  is  to  make.  If  she  writes  one  i on  a  line, 
how  many  lines  will  it  take  ? 

If  you  have  nine  erasers,  and  put  one  at  each  board,  how 
many  boards  can  you  supply  with  erasers  ? 

How  many  days  will  it  take  you  to  earn  nine  cents,  if 
you  earn  a  cent  a  day  ? 

Johnnie  wants  a  watch,  which  costs  five  cents,  and  two 
glass  marbles,  which  are  two  cents  apiece.  If  he  earns  a 
cent  a  day,  in  how  many  days  can  he  earn  enough  to  buy 
the  watch  and  the  glass  marbles? 

Harry  earns  three  cents  a  day,  Willie  only  one  cent  a 
day.  How  many  more  days  will  it  take  Willie  to  earn 
nine  cents  than  it  takes  Harry  ? 

Oranges  are  three  cents  apiece,  plums  only  a  cent  apiece. 
How  many  more  plums  than  oranges  can  you  buy  for  nine 
cents  ? 

How  many  more  vases  at  a  dollar  a  vase  can  I  buy  for 
nine  dollars,  than  vases  at  three  dollars  apiece  ? 


Nine  divided  by  Nine. 

How  many  nine-cent  loaves  of  bread  can  I  buy  for  nine 
cents  ?  How  many  nine-cent  books  ?  How  many  nine-cent 
toys  ?  How  many  nine-cent  pictures  ?  How  many  dozen 
pencils,  at  nine  cents  a  dozen?  How  many  slates,  at  nine 
cents  apiece  ?  How  many  dozen  pens,  at  nine  cents  a  dozen? 
How  many  quarts  of  berries,  at  nine  cents  a  quart?  How 
many  pounds  of  dates,  at  nine  cents  a  pound  ?  How  many 
half-pounds  of  candy,  at  nine  cents  a  half  pound? 


186  FIRST   STEPS   IN   NUMBER. 

If  it  takes  nine  buttons  for  a  boot,  and  Nellie  has  but 
nine  buttons,  how  many  boots  can  she  supply  with  buttons? 

I  have  some  scales  which  will  weigh  anything  not  heavier 
than  nine  pounds.  How  many  packages,  nine  pounds  each, 
can  I  weigh  at  once  with  the  scales  ? 

If  starch  is  put  up  for  sale  in  nine-pound  packages, 
how  many  packages  must  I  buy  to  purchase  nine  pounds  of 
starch  ? 

§  30.   Comparison  of  Nine  with  Numbers  known. 

There  are  nine  little  girls  playing  "  drop  the  handker- 
chief," and  nine  boys  playing  ball.  How  many  more  girls 
than  boys  are  there  ? 

Here  are  nine  cards  on  the  table,  and  there  are  nine  balls 
on  the  desk.     How  many  more  cards  than  balls  are  there  ? 

I  have  two  three-cent  pieces,  and  three  cents ;  Annie  has 
four  two-cent  pieces,  and  one  cent.  Which  has  the  more 
money  ? 

On  my  boot  there  are  nine  buttons ;  on  Nellie's  there  are 
eight.  How  many  more  buttons  are  there  on  my  boot  than 
on  Nellie's? 

I  sold  nine  pencils  to  one  class  this  morning,  and  eight  to 
another  class.  How  many  more  pencils  did  I  sell  to  one 
class  than  to  the  other  ? 

George  has  nine  chickens,  and  eight  ducks.  How  many 
more  chickens  than  ducks  has  he  ? 

There  are  nine  doves  on  the  roof,  and  seven  on  the  walk. 
How  many  more  doves  are  on  the  roof  than  on  the  walk  ? 

Nine  new  tin  pans  have  blown  oif  of  the  bench,  and  seven 
remain  on  the  bench.  How  many  more  have  blown  off 
than  remain  on  the  bench  ? 

Nine  hay-cocks  have  blown  over,  but  seven  are  left  stand- 
ing. How  many  more  have  blown  over  than  are  left  stand- 
ing? 


THE   NUMBER   NINE.  187 

Harry's  bedtime  is  nine  o'clock;  Jennie's  is  seven  o'clock. 
How  many  hour's  later  is  Harry's  bedtime  than  Jennie's  ? 

Sarah  has  picked  nine  quarts  of  strawberries ;  Irene  has 
picked  but  seven  quarts.  How  many  more  quarts  has  Sa- 
rah picked  than  Irene  ? 

A  bicycle  will  run  nine  miles  an  hour ;  a  horse  will  go 
six  miles  an  hour.  How  many  more  miles  an  hour  will  a 
bicycle  go  than  a  horse  ? 

I  bought  some  black-headed  pins  for  nine  cents  a  dozen, 
and  some  needles  for  six  cents  a  paper.  How  much  more 
did  the  dozen  pins  cost  than  the  paper  of  needles  ? 

You  are  to  have  a  vacation  of  nine  weeks ;  I  am  to  have 
one  of  six  weeks.  How  many  more  weeks  do  you  have 
than  I? 

Nine  children  are  busy  doing  number- work ;  six  others 
are  writing.  How  many  more  are  doing  number- work  than 
writing  ? 

It  is  nine  miles  to  the  lake,  and  six  to  the  mountain. 
How  much  farther  is  it  to  the  lake  than  to  the  mountain  ? 

John  earned  nine  dollars  doing  errands  in  vacation ; 
Fred  earned  five  dollars.  How  much  more  money  did 
John  earn  than  Fred? 

In  one  field  there  are  nine  acres ;  in  another  there  are 
only  five  acres.  How  many  more  acres  in  one  field  than  in 
the  other? 

Edward  can  name  nine  dififerent  numbers ;  Susie  can 
name  but  five.  How  many  more  numbers  can  Edward 
name  than  Susie  ? 

Nettie  brought  me  nine  different  kinds  of  leaves  this 
morning.  I  expected  she  could  find  only  five  dififerent 
kinds  of  leaves.  How  many  more  did  she  find  than  I  ex- 
pected she  would  ? 

Bennie  has  finished  nine  pages  of  his  writing-book ;  Liz- 
zie has  finished  but  five  of  hers.  How  many  more  pages 
has  Bennie  written  than  Lizzie  ? 


188  FIRST  STEPS   IN   NUMBER. 

Here  are  riine  blocks,  and  here  are  four  blocks.  How 
many  more  blocks  are  in  one  pile  than  in  the  other  ? 

There  are  nine  lamps  up  and  down  Main  Street;  no 
other  street  in  the  village  has  more  than  four  lamps.  How 
many  more  lamps  has  Main  Street  than  any  other  street  in 
the  village  ? 

There  were  nine  birds'  nests  in  the  trees  about  our  house, 
last  year;  this  year  I  have  seen  but  four.  How  many 
more  were  there  last  year  than  this  ? 

The  train  got  in  at  four  minutes  past  three,  and  left  at 
nine  minutes  past  three.     How  long  did  it  wait  ? 

I  bought  at  the  bakery  a  nine-cent  loaf  of  bread,  and  a 
four-cent  roll.  How  much  more  did  I  pay  for  one  than  for 
the  other  ? 

Ned  bought  a  blank-book  and  a  pencil  this  morning. 
He  gave  nine  cents  for  the  book  and  three  for  the  pencil. 
How  much  more  did  he  give  for  the  book  than  for  the 
pencil  ? 

Alice  is  nine  years  old;  her  little  sister  is  three  years 
old.     How  much  older  is  Alice  than  her  sister  ? 

I  have  a  long,  narrow  book ;  it  is  nine  inches  long,  and 
three  inches  wide.  How  many  more  inches  in  its  length 
than  in  its  width  ? 

In  one  dish  there  are  nine  bunches,  of  grapes,  and  in  an- 
other dish  there  are  three  bunches  of  grapes.  How  many 
more  bunches  in  one  dish  than  in  the  other  ? 

I  bought  a  quart  of  strawberries  for  nine  cents,  and  a 
pint  of  milk  for  three  cents.  How  much  more  did  I  pay 
for  the  strawberries  than  for  the  milk  ? 

I  bought  a  bottle  of  ink  for  nine  cents,  and  a  pen  for  two 
cents.  How  much  more  did  I  pay  for  the  ink  than  for  the 
pen? 

I  have  a  pail  which  holds  four  quarts  and  a  pint.  How 
many  more  pints  does  it  hold  than  a  quart  measure  ? 


THE   NUMBER   NINE.  189 

Jennie  found  nine  straight  pins,  and  two  bent  ones.  How 
many  more  straight  ones  did  she  find  than  bent  ones  ? 

Lilian  has  taken  nine  lessons  on  the  piano,  and  Mary- 
two.    How  many  more  lessons  has  Lilian  taken  than  Mary  ? 

In  the  street-car  to-day  there  were  nine  persons  on  one 
side,  and  two  on  the  other  side.  How  many  more  persons 
were  on  one  side  than  on  the  other  ? 

In  the  harbor  there  are  nine  sail  boats,  and  one  boat 
without  a  sail.  How  many  more  boats  are  there  with  sails 
than  without  ? 

One  hen  has  nine  chickens  ;  another  hen  has  only  one 
chicken.  How  many  more  chickens  has  one  hen  than  the 
other? 

Ida  has  nine  sticks  of  candy,  and  her  little  brother  has 
only  one.  How  many  more  sticks  of  candy  has  Ida  than 
her  brother  ? 

There  were  nine  boys,  and  only  one  little  girl,  in  one  of 
my  classes.  How  many  more  boys  than  girls  were  there  in 
the  class  ? 

There  were  nine  persons  in  our  room  yesterday,  and 
only  one  chair.  How  many  more  persons  than  chairs  were 
there  ? 

Nine  is  how  many  more  than  one  ? 

One  is  how  many  less  than  nine  ? 

Nine  is  how  many  more  than  two  ? 

Two  is  how  many  less  than  nine  ? 

Nine  is  how  many  more  than  three  ? 

Three  is  how  many  less  than  nine  ? 

Nine  is  how  many  more  than  four  ? 

Four  is  how  many  less  than  nine  ? 

Nine  is  how  many  more  than  five  ? 

Five  is  how  many  less  than  nine  ? 

Nine  is  how  many  more  than  six  ? 

Six  is  how  many  less  than  nine  ? 


190  FIRST  STEPS   IN   NUMBER. 

Nine  is  how  many  more  than  seven  ? 

Seven  is  how  many  less  than  nine  ? 

Nine  is  how  many  more  than  eight  ? 

Eight  is  how  many  less  than  nine  ? 

Nine  is  how  many  more  than  nine  ? 

Nine  is  how  many  less  than  nine  ? 

I  have  made  one  pen-wiper.  How  many  more  must  I 
make  to  have  nine  ? 

Hattie  has  two  dolls ;  Jane  has  nine.  How  many  more 
must  Hattie  receive  to  have  as  many  as  Jane  ? 

Flora  has  only  three  words  written;  Alice  has  nine. 
How  many  more  words  must  Flora  write  to  have  as  many 
as  Alice  ? 

I  have  four  cents.  How  many  more  cents  must  I  have 
that  I  may  buy  a  yard  of  cambric  for  nine  cents  ? 

Cyrus  has  five  cents;  his  sister  has  nine  cents.  How 
much  must  Cyrus  earn  that  he  may  have  as  much  money  as 
his  sister? 

Ellen  has  six  picture  books.  How  many  more  must  she 
get  that  she  may  have  nine  ? 

Lottie  is  going  away  to  stay  a  week.  If  she  should  stay 
nine  days,  how  many  days  over  a  week  would  she  stay  ? 

Fred  has  picked  eight  quarts  of  berries.  How  many 
more  quarts  must  he  pick  that  he  may  have  nine  quarts? 

Nine  is  one  more  than  what  number  ? 

Nine  is  eight  more  than  what  number  ? 

Eight  is  one  less  than  what  number  ? 

One  is  eight  less  than  what  number  ? 

Nine  is  two  more  than  what  number  ? 

Nine  is  seven  more  than  what  number  ? 

Seven  is'  two  less  than  what  number  ? 

Two  is  seven  less  than  what  number  ? 

Nine  is  three  more  than  what  number  ? 

Nine  is  six  more  than  what  number  ? 


THE   NUMBER  NINE.  191 

Six  is  three  less  than  what  number  ? 
Three  is  six  less  than  what  number  ? 
Nine  is  four  more  than  what  number  ? 
Nine  is  five  more  than  what  number  ? 
Five  is  four  less  than  what  number  ? 
Four  is  five  less  than  what  number  ? 
Nine  is  nine  more  than  what  number  ? 

Exercise  for  Review. 

I  bought  two  spools  of  thread  at  three  cents  apiece,  and 
three  needles  at  a  cent  apiece.  How  much  did  I  pay  for 
all? 

A  man  bought  a  roll  of  tape  for  five  cents,  and  a  thimble 
for  two  cents,  and  sold  them  for  nine  cents.  How  much 
did  he  gain  ? 

I  sold  a  man  a  pint  of  blueberries  for  four  cents,  and  a 
pint  of  raspberries  for  three  cents,  and  he  sold  each  for  a 
cent  more  a  pint.     How  much  did  he  gain  ? 

A  man  bought  four  paper  dolls  for  a  cent,  and  then  sold 
them  for  a  cent  apiece.     How  much  did  he  gain  ? 

Joseph  bought  a  toy  ship  for  five  cents,  and  a  banana  for 
three  cents,  then  sold  his  ship  for  as  much  as  he  paid  for 
both  ship  and  banana.    How  much  did  he  get  for  his  ship  ? 

A  boy  who  was  selling  fruit  bought  four  pears  for  a  cent, 
and  six  apples  for  a  cent ;  he  sold  his  -pears  for  a  cent 
apiece,  and  his  apples  at  two  for  a  cent,  how  much  did  he 
gain  ? 

A  man  bought  oranges  at  three  cents  apiece,  and  sold 
them  for  five  cents  apiece.  How  much  did  he  gain  on  four 
oranges  ? 

A  merchant  bought  sugar  for  seven  cents  a  pound,  and 
sold  it  for  nine  cents  a  pound.  How  many  pounds  did  he 
have  to  sell  to  gain  eight  cents  ? 


192  FIRST  STEPS   IN   NUMBER. 

I  had  eight  cents,  and  spent  half  of  my  money,  then 
earned  two  cents  more.  If  I  spent  half  of  what  I  then 
had,  how  much  did  I  spend  ? 

A  peck  basket  holds  eight  quarts.  How  many  quarts 
will  a  half-peck  basket  hold  ? 

If  tomatoes  are  three  cents  a  quart,  what  will  three 
quarts  of  tomatoes  cost  ? 

I  bought  a  yard  of  narrow  ribbon  for  three  cents,  a  silver- 
headed  pin  for  two  cents,  and  some  tissue  paper  for  four 
cents.  How  much  did  I  pay  for  what  I  bought  ?  I  gave 
in  payment  three  pieces  of  money  that  were  just  equal  to 
nine  cents.  What  may  the  three  ]3ieces  of  money  have 
been? 

One-half  of  four  apples  put  with  one-half  of  six  apples 
will  make  how  many  apples? 

One-fourth  of  eight  apples  put  with  one-fourth  of  four 
apples  will  make  how  many  apples  ? 

Two-fourths  of  eight  splints  put  with  two-fourths  of  four 
splints  will  make  how  many  splints  ? 

A  toy  balloon  could  be  bought  for  eight  cents.  Eoy  had 
only  one-fourth  enough  money  to  pay  for  it.  How  much 
more  money  did  he  lack  ? 

I  bought  some  fruit  for  eight  cents,  which  was  twice  as 
much  as  I  expected  to  pay  for  it.  How  much  did  I  expect 
to  pay  for  the  fruit  ? 

It  is  two  miles  to  the  village,  and  four  times  as  far  to 
the  beach.  How  much  farther  is  it  to  the  beach  than  to  the 
village  ? 

Lizzie  has  seven  dolls ;  if  she  had  one  more  she  would 
have  twice  as  many  dolls  as  Mary.  How  many  dolls  has 
Mary? 

Mira  has  three  cents.  If  I  had  one  more  cent  I  should 
have  three  times  as  many  cents  as  Mira.  How  many  cents 
have  I  ? 


THE  NUMBER  NINE.  193 

John  can  earn  four  cents  a  day ;  Susie  can  earn  three 
cents  a  day.  How  much  more  money  will  John  earn  in  a 
week  than  Susie  ? 

A  man  bought  two  sheep  at  three  dollars  apiece,  and 
gave  in  payment  a  five-dollar  bill  and  a  two-dollar  bill. 
How  much  money  ought  he  to  receive  back  ? 

I  bought  two  roses  at  two  cents  apiece,  a  bunch  of  violets 
for  three  cents,  and  a  pond-lily  for  a  cent.  I  gave  in  pay- 
ment a  five-cent  piece  and  two  two-cent  pieces.  How  much 
change  ought  I  to  receive  ? 

In  one  nest  there  were  three  eggs,  in  another  two  eggs, 
and  in  another  four  eggs.  If  I  left  the  nest-egg  in  each 
nest,  how  many  eggs  did  I  take  away  ? 

I  can  buy  five  paper-wrappers  for  six  cents ;  each  paper- 
wrapper  has  a  one-cent  stamp  on  it.  How  much  do  I  pay 
for  the  paper  of  which  the  wrappers-are  made  ? 

I  can  buy  four  envelopes  for  five  cents,  each  envelope 
with  a  one-cent  stamp  on  it.  How  much  do  I  pay  for  the 
envelopes  themselves  ? 

I  can  buy  two  envelopes  for  seven  cents,  each  envelope 
with  a  three-cent  stamp  on  it.  How  much  do  I  pay  for  the 
envelopes  themselves  ? 

I  have  a  table  that  is  three  feet  wide,  and  nine  feet  long. 
The  length  of  the  table  is  how  many  times  its  breadth  ? 

One  day  I  read  in  a  book  from  page  three  to  page  nine 
(both  pages  included)  ;    how  many  pages  did  I  read  ? 

Nellie  is  six  years  younger  than  Bennie,  and  four  years 
younger  than  Charlie.  How  much  older  is  Bennie  than 
Charlie? 

We  had  eight  children  to  tea  last  evening ;  they  con- 
sisted of  an  equal  number  of  boys  and  girls.  How  many 
were  boys  ?     How  many  were  girls  ? 

If  a  snail  creeps  three  inches  in  half  a  minute,  how  many 
inches  will  it  creep  in  a  minute  ? 


194  FIRST   STEPS   IN   NUMBER. 

If  I  write  every  morning  from  nine  o'clock  until  twelve 
o'clock,  how  many  hours  shall  I  write  in  three  days  ? 

Each  year  has  a  spring,  a  summer,  an  autumn,  and  a 
winter.  How  many  seasons  are  there  in  a  year  ?  How 
many  seasons  in  two  years  ? 

I  was  at  home  two  years  excepting  one  spring  and  one 
autumn.  How  many  seasons  was  I  at  home  ?  Name  the 
seasons  I  was  at  home. 

If  a  ship  sails  eight  miles  an  hour,  and  a  horse  travels 
six  miles  an  hour,  how  much  farther  than  the  horse  will 
the  ship  go  in  four  hours  ? 

Two  boats  sail  toward  each  other,  each  at  the  rate  of 
three  miles  an  hour.  If  one  starts  an  hour  before  the 
other,  how  much  more  than  half  the  distance  between  the 
two  boats  will  one  boat  go  than  the  other  ? 

Here  are  eight  cents,  with  which  you  may  buy  two 
pounds  of  fish  at  four  cents  a  pound.  How  much  change 
should  you  bring  back  ? 

Here  are  nine  cents  with  which  you  may  buy  three 
pounds  of  soup  beef  at  three  cents  a  pound.  How  much 
change  should  you  bring  back  ? 

Here  is  a  five-cent  piece  and  a  three-cent  piece  which 
you  may  take  to  buy  a  pound  of  mutton  at  seven  cents  a 
pound.     How  much  change  should  you  bring  back  ? 

Here  are  two  three-cent  pieces  which  you  may  take  to 
buy  a  bunch  of  beets  at  five  cents  a  bunch.  How  much 
change  should  you  bring  back  ? 

Here  is  a  five-cent  piece  and  a  two-cent  piece  with  which 
you  may  buy  a  head  of  lettuce  for  six  cents  and  bring  back 
the  money  you  have  left.  How  much  money  will  you  have 
left? 

Here  are  three  three-cent  pieces  which  you  may  take  to 
buy  seven  pounds  of  salt  at  a  cent  a  pound.  How  much 
money  will  you  have  left  ? 


THE   NUMBER   NINE.  195 

Here  are  two  two-cent  pieces  and  a  five-cent  piece  which 
you  may  take  to  buy  tw^o  pounds  of  soup  beef  at  four  cents 
a  pound.     How  much  change  should  you  bring  back  ? 

I  bought  a  bunch  of  beets  for  five  cents  and  paid  for  it 
with  three  pieces  of  money.  What  may  the  three  pieces 
have  been  ? 

I  bought  two  cream  cakes  at  three  cents  each  and  paid 
for  them  with  two  pieces  of  money.  What  were  the  two 
pieces  of  money  if  they  were  equal  ?  if  they  were  unequal  ? 

I  bought  three  bananas  at  three  cents  each  and  paid  for 
them  with  three  pieces  of  money.  What  were  the  pieces 
of  money  if  they  were  equal  ? 

The  sum  of  two  numbers  is  nine,  and  the  smaller  of  the 
two  numbers  is  four ;   what  is  the  larger  of  the  two  numbers? 

The  sum  of  two  numbers  is  nine,  and  the  larger  of  the 
two  numbers  is  seven ;  what  is  the  smaller  of  the  two  num- 
bers? 

The  sum  of  two  numbers  is  nine,  and  the  smaller  of  the 
two  numbers  is  three ;  what  is  the  larger  of  the  two  num- 
bers? 

Tom  has  three  marbles,  and  George  has  three  times  as 
many.     How  many  marbles  has  George  ? 

The  difference  between  two  numbers  is  three,  and  the 
smaller  of  the  two  numbers  is  six  ;  what  is  the  larger  of  the 
two  numbers? 

The  difference  between  two  numbers  is  five,  and  the 
smaller  of  the  two  numbers  is  four ;  what  is  the  larger  of 
the  two  numbers  ? 

The  difference  between  two  numbers  is  one,  and  the 
larger  of  the  two  numbers  is  nine ;  what  is  the  smaller  of 
the  two  numbers  ? 

The  difference  between  two  numbers  is  five,  and  the 
larger  of  the  two  numbers  is  nine ;  what  is  the  smaller  of 
the  two  numbers  ? 


196  FIRST  STEPS  IN   NUMBER. 

One-Third. 

Into  how  many  parts  have  I  divided  this  circle?    (Three.) 

Into  what  kind  of  parts  ?     (Equal  parts.) 

Who  can  fold  this  piece  of  paper  so  as  to  divide  it  into 
three  equal  parts  ? 

Who  can  fold  this  string  so  as  to  divide  it  into  three 
equal  parts  ? 

Divide  this  strip  of  paper  in  the  same  way. 

Shovv  me  one  of  the  three  equal  parts  into  which  the  cir- 
cle was  divided. 

It  is  a  third  of  the  circle. 

Show  me  another  third  of  the  circle. 

Show  me  the  other  third  of  the  circle. 

Show  me  a  third  of  the  strip  of  paper ;  a  third  of  the 
string  ;  two-thirds  of  the  string. 

Divide  this  square  I  have  drawn  on  the  board  into  thirds. 

Divide  the  circle  beside  it  into  thirds. 

Divide  this  triangle  into  thirds  by  drawing  lines  from  the 
vertex  to  the  base. 

Show  me  what  you  think  to  be  one-third  of  this  table  ; 
one-third  of  your  slate  ;  one-third  of  this  desk ;  one-third 
of  this  blackboard  ;  one-third  of  this  three-inch  line.  How 
long  is  one-third  of  the  three-inch  line  ? 

Take  three  blocks.  Divide  the  number  into  three  equal 
parts.     Show  me  one-third  of  three. 

Take  six  blocks.  Divide  the  number  into  three  equal 
parts.     Show  me  one-third  of  six. 

Take  nine  blocks.  Divide  the  number  into  three  equal 
parts.     Hold  up  one-third  of  nine  blocks. 

Who  knows  how  many  one-third  of  three  is  ?  One-third 
of  six  ?     One-third  of  nine  ? 

Write  :  One-third  of  three  is  one.  One-third  of  six  is  two. 
One-third  of  nine  is  three. 


CHAPTEE  IX. 

FIGURES.      GENERAL    REVIEW. 


§31.     Figures  and  Review. 

Write  the  word  that  shows  this  number  (one)  is  meant. 

Who  will  write  the  number  in  another  way  ? 

All  may  make  the  figure  1. 

I  have  three  pencils.  How  many  more  must  I  have  to 
make  five  ? 

I  owe  Ned  five  cents.  I  have  two  three-cent  pieces  which 
I  will  give  him.     How  many  cents  should  he  give  me  back  ? 

Three  things  and  how  many  more  things  make  five 
things  ?  make  seven  things  ?  make  six  things  ?  make  eight 
things  ? 

How  many  fingers  have  you  on  your  right  hand,  beside 
the  thumb?  Put  a  mark  on  the  board  for  each  finger. 
How  many  marks  have  you  made? 

I  will  make  a  figure  for  the  number  you  have  shown  me. 

Hold  up  four  cards.  (Teacher  makes  the  figure  4  on  the 
blackboard.) 

Show  me  four  spools.     (Teacher  makes  the  figure  4.) 

For  how  many  fingers  did  I  make  this  figure  ? 

For  how  many  cards  did  I  make  this  figure? 

For  how  many  spools  did  I  make  this  figure  ? 

What  is  this  figure  ? 


198  FIRST   STEPS    IN   NUMBER. 

Show  me  the  number  of  blocks  for  which  this  figure 
stands ;  the  number  of  sticks  ;  the  number  of  children  ;  the 
number  of  desks. 

How  many  did  you  show  me  in  each  case  ? 

Write  the  word  for  which  this  figure  stands. 

Make  this  figure  on  vour  slates. 


Three  and  three  are  how  many  ? 

Three  and  how  many  are  six  ? 

Four  and  two  are  how  many  ? 

Two  and  how  many  are  six  ? 

Six  minus  three  are  how  many  ? 

Six  minus  two  are  how  many? 

Three  and  how  many  are  five  ? 

One-half  of  six  is  how  many  more  than  one-half  of  four  ? 

One-half  of  six  and  one-half  of  four  are  how  many  ? 

I  have  here  two  three-cent  stamps.  How  much  money 
did  they  cost  ?  I  paid  for  them  with  two  pieces  of  money. 
What  may  the  two  pieces  of  money  have  been  ? 

I  bought  two  oranges  last  week  at  three  cents  apiece. 
What  change  ought  I  to  have  received,  if  I  gave  in  pay- 
ment two  two-cent  pieces  and  a  three-cent  piece  ? 

John  went  down  to  his  father's  shop  four  times  in  the 
morning,  and  twice  in  the  afternoon.  How  many  times 
did  he  go  altogether  ? 

Four  baby  carriages  and  how  many  more  baby  carriages 
make  six  baby  carriages  ? 

Two  and  how  many  more  are  six  ? 

Six  pieces  of  pie  less  four  pieces  of  pie  leave  how  many 
pieces  of  pie  ? 

Six  peanuts  less  two  peanuts  leave  how  many  peanuts  ? 

How  many  pints  in  three  quarts? 


FIGURES.     GENERAL  REVIEW.  I99 

If  you  have  two  pints  of  milk,  how  many  quarts  of  milk 
must  you  buy  that  you  may  have  six  pints  of  milk? 

We  get  six  eggs  every  day.  If  we  use  two  in  the  morn- 
ing and  two  at  noon,  how  many  are  left  ? 

Mary  has  four  dollars ;  I  have  six.  How  many  more 
dollars  have  I  than  Mary  ? 

How  much  money  must  I  pay  for  three  two- cent  stamps? 
for  three  three-cent  stamps  ?  for  nine  one-cent  stamps  ?  for 
a  half  dozen  postal  cards  ?  for  a  five-cent  stamp  and  two 
two-cent  stamps? 

Find  all  the  twos  you  can  in  six.  All  the  threes  you 
can  in  six.     Show  me  one-half  of  six ;  one-third  of  six. 

Tell  me  a  story  for  what  I  show  you. 


Put  seven  marks  on  the  board. 

Write  the  word  seven. 

This  is  the  figure  7. 

Show  me  the  number  of  marks  for  which  this  figure 
stands. 

Show  me  the  word  that  means  the  same  as  this  figure. 

See  how  many  blocks  I  show  you.     (Seven.) 

Make  the  figure  that  shows  this  number  is  meant. 

Make  the  figure  that  shows  this  number  of  balls  is  meant. 
(Seven.) 

This  number  of  shells.     (Seven.) 

This  number  of  shells.     (One.) 

This  number  of  shells.     (Four.) 

How  many  different  figures  have  you  made  ?  Which  is 
the  prettiest  ?  Which  is  the  easiest  to  make  ?  Which 
stands  for  the  most  things  ?  Which  can  you  do  quickest, 
put  seven  marks  on  the  board,  write  the  word  seven,  or 
make  the  figure  7  ? 


200  FIRST  STEPS   IN   NUMBER. 

I  have  four  cents  and  Eva  has  five  cents.  We  are  going 
to  put  our  money  together  to  buy  some  sweet  crackers. 
How  many  cents'  worth  of  crackers  can  we  buy  ? 

Five  oyster- shells  and  four  oyster-shells  are  how  many 
oyster-shells? 

Tell  me  a  story  for  five  and  four. 

If  you  have  nine  apples  and  I  have  five  apples,  how 
many  more  have  you  than  I  ? 

If  you  give  me  two  of  your  apples,  who  will  have  the 
greater  number  then  ? 

Nine  less  two  are  how  many  more  than  five  and  two  ? 

Ealph  has  nine  cents.  Lizzie  has  five  cents.  How  many 
cents  must  Ralph  give  Lizzie  that  each  may  have  the  same 
number  ? 

In  an  orchard  there  are  nine  trees.  If  there  are  two 
rows  of  four  trees  each,  how  many  trees  are  there  besides? 
Six  of  these  trees  blossomed.    How  many  had  no  blossoms  ? 

I  have  in  my  purse  a  five-cent  piece  and  two  two-cent 
pieces.  How  many  cents  have  I  in  my  purse  ?  I  shall 
spend  my  five-cent  piece  for  a  bottle  of  ink.  How  many 
cents  shall  I  then  have  ? 

Mary  is  nine  years  old  and  Harry  is  seven.  How  much 
older  than  Harry  is  Mary  ?  Annie  is  two  years  old.  How 
much  older  than  Annie  is  Mary  ? 

I  have  here  three  rows  of  beans  with  three  beans  in  a 
row.     How  many  beans  have  I  ? 

I  have  nine  cents  and  Eva  has  three  three- cent  pieces. 
Which  one  of  us  is  the  richer  ? 

If  one  spool  of  thread  costs  three  cents,  what  will  three 
spools  of  thread  cost  ? 

How  much  will  three  pints  of  milk  cost  at  three  cents  a 
pint? 

It  took  a  man  a  week  and  three  days  to  lay  a  piece  of 
wall.     How  many  days  did  it  take  him  ? 


FIGURES.      GENERAL   REVIEW.  201 

If  I  can  earn  a  cent  every  day,  how  many  days  over  a 
week  must  I  work  to  earn  nine  cents  ? 

If  a  boy  earns  a  dollar  a  month,  and  spends  half  of  what 
he  earns  each  month,  how  many  months  must  he  work  to 
save  four  dollars  ? 

If  a  newsboy  buys  a  paper  for  four  cents  and  sells  it  for 
five  cents,  how  many  papers  must  he  sell  to  gain  eight  cents  ? 

A  boy,  who  buys  apples  at  the  rate  of  three  for  two  cents, 
sells  his  apples  at  a  cent  apiece.  How  many  cents  does  he 
gain  on  three  apples  ?  How  many  cents  does  he  gain  on 
twice  three  apples  ? 


Make  nine  marks  on  the  board. 

Write  the  word  that  stands  for  nine. 

Does  any  one  know  the  figure  that  shows  nine  is  meant  ? 

I  will  make  it  for  you. 

Show  the  number  of  blocks  for  which  this  new  figure 
stands. 

I  will  show  you  a  number  of  things,  and  you  may  write 
the  figure  that  stands  for  it : 

Nine  ;  one  ;  four  ;  seven  ;  nine ;  four ;  nine. 

Name  these  figures  as  I  point : 

1;  7;  9;  4;  7;  9;  4. 


Tell  me  a  story  for : 

Three  minus  three.  Six  minus  six. 

Six  and  three.  Five  and  four. 

Four  and  three.  Nine  minus  seven. 

Seven  minus  fiYe,  Six  divided  by  two. 

Two  twos.  Three  threes. 

Two  threes.  Four  twos. 

Three  twos.  Two  fours. 


202  FIRST  STEPS   IN   NUMBER. 

Half  a  pound  of  sugar  costs  four  cents.  What  does  a 
pound  cost  at  that  rate  ? 

I  bought  two  oranges  for  eight  cents.  One  orange  cost 
two  cents  more  than  the  other.  What  was  the  price  of 
each? 

If  I  divided  four  oranges  among  some  boys,  giving  them 
half  an  orange  apiece,  to  how  many  boys  did  I  give  them  ? 

I  gave  a  five-cent  piece  and  a  three-cent  piece  for  two 
quarts  of  milk.  What  was  the  cost  of  a  pint  of  milk  at  that 
rate? 

I  measured  out  a  quart  of  water  with  a  gill  cup.  How 
many  times  did  I  have  to  fill  the  gill  cup  ? 

If  a  pint  of  milk  costs  two  cents,  what  will  two  gills  cost 
at  the  same  rate  ? 


If  I  spend  all  my  money,  how  much  money  shall  I  have 
left  ?  You  say  I  shall  have  none  left.  I  will  put  on  the 
board  the  figure  0,  which  always  shows  that  none  is  meant. 
Its  name  is  zero. 

Tell  me  what  you  see  in  this  room  like  it.  (Eye-glasses ; 
handle  of  a  mug  ;  letter  0  on  the  board.) 

Make  the  figure  with  your  forefinger  and  thumb.  Put  it 
up  to  your  eyes  so  that  you  can  look  through  the  opening. 
What  shape  has  your  eye  ? 

Notice  what  I  do.  (Show  three  blocks,  and  then  remove 
them  from  sight.) 

What  is  the  answer  ?     (None.) 

Show  me  the  figure  that  stands  for  none. 

Give  me  an  example  such  that  the  answer  can  be  shown 
by  this  figure. 

I  had  seven  chickens.  I  sold  five  and  then  I  sold  two. 
How  many  had  I  left  ?  Put  on  the  board  the  figure  that 
shows  how  many. 


FIGURES.      GENERAL   REVIEW.  208 

I  had  five  minutes  to  wait  at  a  railroad  station.  It  took 
me  three  minutes  to  get  my  ticket  and  two  minutes  to  say 
"good  bye"  all  round.     How  many  minutes  had  I  left  ? 

Express  the  answer  on  the  board. 

Show  me  the  figure  that  stands  for  one  more  than  none ; 
that  stands  for  four  more  than  none ;  that  stands  for  seven 
more  than  none  ;  that  stands  for  nine  more  than  none  ;  that 
stands  for  none. 

Make  all  the  figures  you  know  on  your  slate,  and  write 
against  each  figure  its  name. 


Two  twos  are  how  many  ? 
Three  twos  are  how  many  ? 
Four  twos  are  how  many  ? 
Two  threes  are  how  many  ? 
Three  threes  are  how  many  ? 
Two  fours  are  how  many  ? 
One-third  of  six  is  how  many  ? 
One-third  of  nine  is  how  many  ? 
One-fourth  of  four  is  how  many  ? 
One-fourth  of  eight  is  how  many? 
Tell  me  a  story  for : 

Three  and  four.  Nine  minus  four. 

Seven  minus  four.  Nine  minus  five. 

Seven  minus  three.         Five  and  three. 
Four  and  five.  Eight  minus  three. 


Name  two  numbers  which  together  make  six. 
Who  can  make  the  figure  6  ? 
Express  on  the  board  the  numbers  I  show  you : 
Six  ;  seven  ;  six  ;  nine  ;  four  ;  six  ;  nine. 
Name  each  figure  as  I  point.     Which  figure  expresses 
the  most? 

Make  the  figure  6  on  your  slates. 


204  FIRST   STEPS  IN   NUMBER. 

Read  what  I  show  with  the  blocks.  (Six  and  one  are 
seven.) 

Write  this  expression,  using  figures  for  six,  one,  and 
seven.     (The  expression  stands:    6  and  1  are  7.) 

Read  what  you  have  written. 

Read  what  I  show  with  the  blocks.  (Seven  minus  one 
are  six.) 

Express  this,  using  figures.     (7  minus  1  are  6.) 

Read  what  you  have  written. 

Copy  these  two  expressions  on  your  slates. 


Think  of  a  story  whose  answer  i^five. 

Who  can  put  the  figure  6  on  the  board  ? 

Write  its  name.  Show  me  the  number  of  marks  for 
which  it  stands.     What  is  the  figure  ? 

Read  what  I  show  you.     (Four  and  one  are  five.) 

Express  this,  using  figures  for  the  numbers.  (4  and  1 
are  5.) 

Read  what  you  have  written. 

Read  what  I  write : 

4  and  1  are  5.  5  minus  4  is  1. 

5  and  4  are  9.  9  minus  4  are  5. 
1  and  4  are  5.  9  minus  5  are  4. 

5  and  1  are  6.  7  minus  1  are  6. 

6  and  1  are  7.  6  minus  5  is  1. 

Express  with  figures  what  I  show  you  with  the  blocks : 
Five  minus  one  are  four. 
Six  minus  one  are  fiYQ. 
Five  minus  five  is  zero. 
Nine  minus  nine  is  zero. 
Seven  minus  seven  is  zero. 


FIGURES.  GENERAL   REVIEW.                       205 

Finish  the  sentences,  using  figures : 

6  and  1  are  5  and  4  are 

4  and  1  are  6  and  1  are 

5  and  1  are  7  minus  1  are 
4  and  5  are  9  minus  4  are 
9  minus  5  are  5  minus  1  are 

7  and  0  are  9  minus  9  is 
9  and  0  are  5  minus  5  is 
7  minus  6  is  5  minus  4  is 


Draw  a  line  two  inches  long.  Divide  the  line  into  two 
equal  parts.  Erect  a  square  on  each  half.  How  many- 
squares  have  you  drawn  ? 

Write  the  word  iivo.  Express  two  in  some  other  way. 
Who  knows  the  figure  2  ?     I  will  make  it  for  you. 

Point  to  the  figure  that  stands  for  this  number.     (Two.) 
Make  the  figure  that  stands  for  this  number.    (Two.) 
Make  the  figure  for  each  of  the  numbers  I  show  you. 
I  will  name  a  number,  and  you  may  point  to  the  figure 
that  stands  for  the  number:    One,  Two,  Four,  Five,  Six, 
Seven,  Nine,  None. 


Express  in  figures  the  answers  to  these  examples  I  give 
you. 

If  you  model  in  clay  five  flowers  and  two  animals,  how 
many  forms  will  you  have  modelled  ? 

If  two  of  the  flowers  should  crack  into  pieces,  and  you 
should  model  four  more  forms,  how  many  forms  would  you 
then  have  ? 

Eight  boats  were  drying  in  the  sun  yesterday.  To-day 
there  are  only  half  as  many.  How  many  boats  are  drying 
in  the  sun  to-day  ? 


206  FIRST  STEPS   IN   NUMBER. 

There  were  nine  panes  of  glass  in  tlie  upper  sash  of  a 
window,  but  four  panes  were  broken  by  a  swinging  blind. 
How  many  panes  remained  unbroken  ? 

I  see  that  Harry  has  nine  peanuts.  If  he  gives  me  a 
third  of  what  he  has,  how  many  will  he  have  left  ? 

There  are  nine  pencils  on  my  desk.  Four  of  them  have 
rubber  tops,  three  have  ivory  tops,  two  have  nothing  on 
the  top,  and  the  rest  have  gold  tops.  How  many  have 
gold  tops? 

Eight  children  are  at  the  board.  Two  are  drawing,  ^ve 
are  writing,  and  the  rest  seem  to  be  doing  nothing.  How 
many  are  idle  ? 

Harry  has  made  nine  designs  with  his  sticks.  Victor  has 
made  seven  designs.  How  many  more  designs  must  Victor 
make  to  have  as  many  as  Harry  ? 


Write  in  words  the  answers  to  these  examples  I  give 
you: 

There  were  six  hens  in  the  garden  a  moment  ago,  but 
half  of  them  have  gone  to  roost.  How  many  are  in  the 
garden  now  ? 

I  have  eight  cents  in  my  pocket  in  two  pieces  of  money. 
One  of  the  pieces  of  money  is  a  five-cent  piece.  What  is 
the  other  piece  of  money  ? 

Two  days  of  last  week  were  too  cold,  two  were  too  warm, 
and  the  rest  of  the  week  was  very  pleasant.  How  many 
days  were  pleasant  ? 

What  word  have  you  written  each  time  ?  (Three.)  Who 
will  express  three  in  some  other  way  ?  Ned  has  made  the 
figure  3.  All  make  the  figure  3.  All  show  me  the  number 
of  fingers  for  which  the  figure  stands  ;  the  number  of 
blocks ;  the  number  of  pieces  of  crayon ;  the  number  of 
panes  of  glass. 


FIGURES.      GENERAL   REVIEW.  207 

Nellie  may  name  a  number,  and  tlie  class  express  it. 
Addie  may  name  a  number.  Jennie  may  name  a  number. 
Ned  may  name  three  numbers. 

Willie  may  point  to  tbe  figures,  and  the  class  may  name 
them. 

Finish  the  sentences  I  have  begun : 

4  and  3  are  9  minus  2  are    . 

3  and  2  are  7  minus  3  are 

5  and  2  are  7  minus  2  are 

6  and  3  are  6  minus  2  are 

4  and  2  are  6  minus  3  are 
9  minus  3  are  5  minus  3  are 

2  twos  are  2  threes  are 

3  twos  are  7  ones  are 
3  threes  are                       3  ones  are 


What  number  added  to  five  will  give  eight  ?  added  to 
four  ?  added  to  three  ?  added  to  six  ?  added  to  one  ?  added 
to  two  ? 

Think  of  two  numbers  which  added  together  will  give 
eight  for  the  answer. 

What  number  made  less  by  four  is  four  ?  made  less  by 
three  is  five  ?  made  less  by  two  is  six  ?  made  less  by  seven 
is  one  ?  made  less  by  eight  is  none  ? 

Who  knows  what  figure  to  write  for  eight?  Write  the 
figure  8. 

Who  has  a  story  whose  answer  is  eight  ? 

Write  eight  figures  that  you  know. 

Name  the  figures  you  have  written. 

Write  two  more  figures  that  you  know. 

Name  the  figures  as  I  point. 

When  I  point  to  a  figure,  you  may  point  to  one  that  stands 
for  two  more  than  the  figure  to  which  I  point. 


208                             FIRST  STEPS    IN   NUMBER. 

Show  me  with  the  blocks  what  these  stories  mean : 

4  and  4  are  8.  8  minus  4  are  4. 

5  and  3  are  8.  8  minus  5  are  3. 

7  and  1  are  8.  8  minus  2  are  6. 

6  and  2  are  8.  8  minus  1  are  7. 

3  and  5  are  8.  8  minus  3  are  5. 

4  twos  are  8.  8  divided  by  2  are  4. 
2  fours  are  8.  8  divided  by  4  are  2. 

8  ones  are  8.  8  divided  by  1  are  8. 


Express  in  figures  the  answers  to  these  examples  I  give : 

A  wood  sawyer  cuts  each  stick  into  three  pieces.  How 
Aiany  cuts  does  he  make  in  sawing  a  stick  of  wood  ?  in 
sawing  two  sticks  of  wood  ?  in  sawing  four  sticks  of  wood  ? 

If  peaches  are  selling  at  the  rate  of  two  for  a  cent,  how 
many  peaches  can  I  buy  for  four  cents  ?  for  two  cents  ?  for 
three  cents  ?  At  the  same  rate  how  much  will  six  peaches 
cost?  will  eight  peaches  cost?  will  four  peaches  cost? 

Jessie  is  two  years  old  to-day.  In  how  many  years  will 
she  be  twice  as  old  as  she  now  is?  In  how  many  years  will 
she  be  four  times  as  old  as  she  now  is  ? 

Four  years  ago  Mary  was  only  half  as  old  as  she  now  is. 
How  old  is  she  now?     How  old  was  she  four  years  ago? 

In  three  years  Bessie  will  be  twice  as  old  as  she  now  is. 
How  old  is  Bessie  now  ? 

A  boy  worked  at  haying  for  a  dollar  a  day.  How  many 
dollars  did  he  earn  in  working  a  week  and  a  half? 

Harry  said  to  Tom,  ''I  have  three  torpedoes  left;  how 
many  have  you?"  Tom  answered,  ''  I  have  twice  as  many 
as  you,  and  one  more;  guess  how  many  I  have."  How 
many  do  you  guess  Tom  had  ? 

How  many  half-pound  weights  must  be  placed  in  one 
scale-pan  to  balance  four  and  a  half  pounds  of  shot  in  the 
other  scale-pan? 


FIGURES.      GENERAL   REVIEW.  209 

If  a  locomotive  goes  at  tlie  rate  of  half  a  mile  a  minute, 
how  many  miles  will  it  go  in  eight  minutes  ?  At  the  same 
rate,  how  long  will  it  take  a  locomotive  to  go  two  and  a 
half  miles  ?  three  and  a  half  miles  ?  four  and  a  half  miles  ? 

I  saw  on  a  shelf  in  a  tin-shop  a  quart  pan,  and,  arranged 
around  the  pan,  as  many  gill  cups  as  would  be  required  to 
hold  as  much  as  the  quart  pan.  How  many  gill  cups  were 
arranged  around  the  pan  ? 


What  part  of  this  circle  do  I  show  you  ?   (One-half.) 

What  part  of  this  square  ?    (One-half.) 

What  part  of  two  is  one  ? 

What  part  of  four  is  two  ? 

What  part  of  six  is  three  ? 

What  part  of  eight  is  four  ? 

Who  can  express  one-half  on  the  hoard,  using  figures? 

I  will  express  it.     Read  what  I  write  : 

i  of  2  is  1.  J  of  6  is  3. 

J  of  4  is  2.  i  of  8  is  4. 

One-half  of  1  is  one-half. 
Express  the  last  sentence,  using  this  new  sign,  ^. 
Complete  these  sentences : 

J  of  8  is  J  of  a  quart  is 

J  of  2  is  }  of  a  pint  is 

3  is     of  6.  1  pint  is     of  a  quart. 

4  is     of  8.  2  gills  are      of  a  pint. 


Express  in  figures  the  answers  to  these  examples : 

A  hen  had  eight  chickens.     One  got  drowned,  and  one 

always  fctays  in  the  coop  with  its  mother.     How  many 

chickens  go  wandering  off  by  themselves? 

If  three  of  the  six  get  into  the  garden,  what  part  of  the 

number  is  in  the  garden  ? 


210  FIRST   STEPS   IN   NUMBER. 

How  many  handles  liave  four  trunks,  if  two  of  them 
have  but  one  handle  each  ? 

How  much  will  the  stamps  for  four  letters  cost,  if  two 
letters  require  but  a  cent  stamp  each  ? 

If  two  men  saw  three  cords  of  wood  in  a  day,  how  many 
cords  of  wood  will  they  saw  in  three  days? 

If  three  newspapers  sold  for  nine  cents,  what  was  the 
price  of  each  newspaper? 

If  six  apples  sold  for  three  cents,  what  was  the  price  of 
one  apple  ? 

What  will  three  and  a  half  yards  of  edging  cost,  at  two 
cents  a  yard  ? 

Four  cents  will  buy  how  many  plums,  at  half  a  cent 
each  ? 

Three  cents  will  buy  how  many  paper  dolls,  if  two  can 
be  bought  for  a  cent  ? 

Nine  cents  will  buy  how  many  five-cent  whistles  ?  how 
many  more  cents  are  needed  to  buy  another  whistle  ? 

Eight  cents  will  buy  how  many  five-cent  bags  of  pop- 
corn ?  How  many  more  cents  are  needed  to  buy  another 
bag  of  pop-corn.  , 

Divide  this  line  into  four  equal  parts.     What  part  of  this 
whole  line  is  each  part,  if  you  have  divided  the  line  equally  ? 
Who  knows  how  to  express  one-fourth,  using  figures  ? 
All  write  one-fourth  this  new  way,  \. 
Eead  what  I  have  written  : 

^  of  4  is  1.  1  gill  is  -i-  of  1  pint. 

^  of  8  is  2.  2  gills  are  -^  of  1  quart, 

1  is  ^  of  4.  i  of  1  pint  is  1  gill. 

2  is  -^  of  8.  ^  of  1  quart  is  2  gills. 
Divide  the  square  that  I  have  drawn  on  the  board  into 

eight  equal  triangles. 

What  part  of  the  square  is  each  triangle  ? 


FIGURES.      GENERAL   REVIEW. 


2U 


Who  can  express  one-eighth  a  new  way  ? 

Ned  may  express  one-eighth  the  new  way  in  each  triangle. 

All  express  :  \;  \\  \. 


Write:   i  of  8  is  1. 

|-  of  1  quart  is  '. 

L  gill. 

1  is  i  of  8. 

1  gill  is  -|-  of  1  quart. 

i  and  \  are  |. 

f  minus  \  is  \. 

\  and  \  are  f . 

■|  minus  \  is  \. 

1  and  \  are  f . 

f  minus  \  is  f . 

1  and  ^  are  f . 

f  minus  \  is  f . 

^  and  ^  are  1. 

\  minus  |-  is  0. 

f  and  1  are  1. 

1  niinus  J  is  f . 

|-  and  f  are  1. 

1  minus  1-  is  ^. 

Who  will  express  one-third  a  new  way  ?     Express  it. 

Write  :   -^  of  3  is  1. 

3  is  i  of  9. 

I'isiofS. 

i  and  \  are  |. 

1  of  6  is  2. 

f  and  \  are  1. 

2  is  1  of  6. 

f  minus  -|-  is  -1-. 

^  of  9  is  3. 

1  minus  f  is  0. 

Read  what  you  have  written. 

Finish  these  sentences : 

^  of  2  is  . 

^  of  1  quart  is 

pint. 

-|-  of  4  is 

|-  of  1  quart  is 

gills. 

^  of  6  is 

\oil  quart  is 

gills. 

1  of  8  is 

•J-  of  1  pint    is 

gills. 

^  of  1  is 

J  of  1  pint    is 

gill. 

■^  of  4  is 

•|-  of  1  quart  is 

gill. 

i  of  8  is 

1  is  i  of 

1  of  8  is 

2  is  1  of 

1  of  3  is 

3  is  1  of 

1  of  6  is 

4  is  1  of 

i  of  9  is 

1  is  i  of 

1  is  1  of 

2  is  i  of 

2  is  1  of 

1  is  1  of 

CHAPTEE  X. 

THE   NUMBER  TEN.     THE  SIGNS:  =, -f-, --. 


§32.     The  Number  Ten. 

Place  nine  blocks  on  the  table  in  front  of  you.  Put  one 
more  block  with  them.  Who  knows  how  many  blocks  nine 
blocks  and  one  block  are  ? 

Nine  blocks  and  one  block  are  ten  blocks. 

Nine  splints  and  one  splint  are  how  many  splints  ? 

Nine  horses  and  one  horse  are  how  many  horses  ? 

Nine  balls  and  one  balloon  are  how  many  toys  ? 

Tell  me  a  story  for  nine  and  one. 

On  one  side  of  a  building  there  is  an  opening  left  for  the 
door,  and  nine  openings  left  for  windows.  How  many 
openings  are  on  that  side  of  the  building  ? 

One  star  shone  out  in  the  sky  almost  as  soon  as  the  sun 
was  set,  and  soon  I  counted  nine  more  stars.  How  many 
stars  were  to  be  seen  then  ? 

I  saw  an  ant  trying  to  carry  oiF  a  big  bug,  but  it  was  too 
heavy  for  him  ;  and  so  another  ant  came  to  help  him,  and 
then  another,  and  another,  until  at  last  nine  other  ants 
had  come  to  help  the  first  ant.  How  many  ants  were  then 
carrying  away  the  bug? 

How  many  fingers  and  thumbs  have  you  on  both  hands  ? 
If  you  had  but  one  thumb,  how  many  fingers  and  thumbs 
would  you  have  on  both  hands  together  ? 

In  a  brood  of  ten  chickens,  one  chicken  was  white  and 
the  rest  were  black.     How  many  were  black  ? 


THE   NUMBER   TEN.  213 

Make  ten  straight  marks  on  the  board.  Cover  nine  of 
them  with  the  eraser.     How  many  marks  are  not  covered  ? 

Here  is  a  ten-cent  piece  which  you  may  take  to  buy  three 
bananas  at  three  cents  each.  How  much  money  should 
you  return  to  me  ? 

If  you  buy  a  yard  and  a  half  of  cambric  at  six  cents  a 
yard,  and  give  a  ten-cent  piece  in  payment,  how  much 
money  ought  you  to  receive  back? 

I  bought  a  bunch  of  envelopes  for  five  cents,  and  two 
pencils  at  two  cents  each.  I  gave  in  payment  a  ten-cent 
piece.     How  much  change  ought  I  to  receive  ? 

I  can  ride  ten  miles  on  my  ticket.  If  I  ride  six  miles  out 
and  half  way  back,  how  many  more  miles  can  I  ride  on  my 
ticket? 

How  many  one-cent  stamps  can  I  buy  for  ten  cents? 

How  many  postal  cards  can  I  buy  for  ten  cents  ? 

How  many  sticks  of  candy  can  I  buy  for  ten  cents  ? 

How  many  rolls  of  lozenges,  at  a  cent  a  roll,  can  I  buy 
for  ten  cents? 

How  many  buns,  at  a  cent  a  bun,  can  I  buy  for  ten  cents? 

What  will  ten  glass  balls  cost,  at  a  cent  a  ball  ? 

What  will  ten  pens  cost,  at  a  cent  a  pen  ? 

What  will  ten  one-cent  books  cost  ? 

If  there  is  a  mirror  in  each  one  of  ten  rooms  in  a  house, 
how  many  mirrors  are  in  the  house  ? 

An  old  clock-maker  was  very  fond  of  buying  old  and 
curious  clocks.  He  had  one  in  each  one  of  the  ten  rooms 
in  his  cottage.     How  many  clocks  had  he  ? 

How  many  ten-cent  loaves  of  bread  can  be  bought  for 
ten  cents? 

How  many  sets  of  paper  dolls,  at  ten  cents  a  set,  can  be 
bought  for  ten  cents  ? 

How  many  picture-books,  at  ten  cents  each,  can  be  bought 
for  ten  cents  ? 


214  FIRST  STEPS   IN   NUMBER. 

Notice  how  I  express  ten  in  figures. 

What  figure  have  I  made?     (The  figure  1.) 

What  figure  have  I  now  placed  against  the  1  ?  (The 
figure  0.) 

These  two  figures  show  that  ten  is  meant. 

All  raise  right  hands.  Who  will  tell  me  on  which  side 
of  1  the  0  stands  ? 

All  write  ten  in  figures,  and  think  that  the  zero  is  on  the 
right-hand  side  of  the  figure  1. 

Write  in  figures  what  I  show  you  with  the  blocks: 

Nine  and  one  are  ten. 
Ten  minus  one  are  nine. 
Ten  minus  nine  is  one. 
One  and  nine  are  ten. 
Ten  ones  are  ten. 
Ten  divided  by  one  are  ten. 


The  Sign  =. 

Who  will  supply  the  word  that  is  needed  to  complete 
these  sentences? 


5  and  3 

8. 

7  minus  4 

3. 

9  and  1 

10. 

10  minus  1 

9. 

4  and  3 

7. 

9  minus  6 

3. 

3  threes 

9. 

9  minus  7 

2. 

4  twos 

8. 

10  divided  by 

1 

10. 

2  fours 

8. 

9  divided  by 

3 

3. 

0  ones 

10. 

8  divided  by 

4 

2. 

I  will  show  you  a  new  way  to  make  the  board  say  "  are  " 
in  these  sentences.     This  sign  =  stands  for  are. 

Put  this  mark  where  it  belongs  in  the  first  sentence,  and 
read  the  sentence.  In  the  second  sentence,  and  read.  In 
the  next  sentence,  and  read.     Fill  each  blank,  and  read. 


THE  NUMBER  TEN. 


215 


Complete  these  sentences : 

5  minus  3  =^ 

3  and  2  = 

4  and  2  = 

6  minus  4  = 

2  and  5  = 

7  minus  5  = 

3  and  4  -- 

9  minus  6  = 

9  divided  by  3  = 

8  divided  by  2= 

9  and  1  = 
1  and  9  = 


7  minus  3  = 

7  minus  4  = 

3  and  5  — 

4  and  5  = 

8  minus  5  = 

9  minus  7  = 
9  minus  5  = 

6  divided  by  2  = 
8  divided  by  4  = 
6  divided  by  3  = 
10  minus  1  = 
10  minus  9  = 


Show  me  eight  fingers. 

How  many  more  fingers  have  you  ? 

Eight  fingers  and  two  fingers  are  how  many  fingers  ? 

Find  if  it  is  true  that  eight  blocks  and  two  blocks  are 
ten  blocks ;  that  eight  paper  disks  and  two  paper  disks  are 
ten  paper  disks. 

Tell  me  stories  for  eight  and  two. 

On  my  rosebush  there  are  two  roses  and  eight  buds. 
How  many  buds  and  blossoms  are  on  my  bush  ? 

In  an  excursion  party  there  were  two  gentlemen  and 
eight  ladies.     How  many  persons  were  in  the  party  ? 

Eddie  is  two  years  old,  and  Frank  is  eight.  If  I  give 
to  each  as  many  cents  as  he  is  years  old,  how  many  cents 
shall  I  gi^  to  both? 

If  I  have  ten  cents  to  spend,  and  buy  a  whistle  for  two 
cents,  how  many  cents  shall  I  have  left  ? 

If  there  were  ten  cakes  on  the  plate,  and  two  were  eaten, 
how  many  cakes  were  left  on  the  plate? 

I  bought  a  pen-holder  for  ten  cents,  and  Mary  bought 
one  for  two  cents  less.     How  much  did  Mary  pay  ? 


216  FIRST   STEPS   IN   NUMBER. 

Tell  me  a  story  for  ten  minus  two. 

There  were  ten  lambs  in  a  flock.  Eight  of  them  were 
white  and  the  rest  black.     How  many  were  black  ? 

In  an  orchard  there  are  ten  rows  of  trees.  Eight  rows 
are  young  trees,  and  the  other  rows  are  old  trees.  How 
many  rows  of  old  trees  are  there  ? 

Last  week  berries  sold  for  ten  cents  a  quart.  This  week 
they  are  selling  for  eight  cents  a  quart.  What  is  the  dif- 
ference in  price? 

Who  has  a  story  for  ten  minus  eight. 

Take  ten  blocks.  Call  them  horses.  Arrange  them  in 
spans.  How  many  spans  of  horses  are  there  ?  Call  them 
oxen.     How  many  yokes  of  oxen  are  there? 

I  have  ten  cents  in  two-cent  pieces.  How  many  two- 
cent  pieces  have  I  ? 

If  a  milliner  uses  two  yards  of  ribbon  for  a  pair  of  bon- 
net-strings, how  many  pairs  of  bonnet-strings  will  ten 
yards  of  ribbon  make  ? 

On  a  piece  of  road,  stone  posts  were  erected  every  two 
miles.  How  many  posts  would  one  pass  in  going  ten  miles 
on  that  road? 

I  have  ten  quarts  of  milk.  How  many  two-quart  cans 
can  I  fill? 

Show  me  five  rows  of  buttons,  two  buttons  in  each  row. 
How  many  buttons  do  you  show  me  ? 

If  there  are  five  birds,  and  each  bird  finds  two  worms, 
how  many  worms  will  they  find  together  ? 

If  there  are  five  nests,  and  two  birds  in  a  nest,  how 
many  birds  are  there  altogether  ? 

I  saw  five  street-cars  go  by  with  only  the  driver  and 
conductor  in  each  car.  How  many  men  were  there  on  all 
the  cars  together  ? 

Five  bicycles  have  how  many  wheels  ? 

In  five  dollars  how  many  half-dollars? 


THE  NUMBER  TEN.  217 

Give  an  example  for  what  I  express  on  the  board : 
8  and  2  =  10.  10  minus  8  --  2. 

2  and  8  =  10.  10  divided  by  2  ==  5. 

10  minus  2  =  8.  5  twos  =  10, 

The  Sign  -f  • 

Who  will  supply  the  word  that  is  needed  to  complei^ 
these  sentences  ? 

8         2=10.  2         8  =  10. 

5         4  =  9.  6         3  =  9. 

5        3  =  8.  2        7  =  9. 

4        3  =  7.  2        6  =  8. 

Instead  of  writing  the  word  "  and,"  we  can  make  a  mark 
which  always  shows  that  and  is  meant.  It  is  this,  + .  Who 
will  describe  this  sign  ? 

Put  it  in  the  first  sentence,  where  you  would  put  the  word 
"and,"  and  read  the  sentence. 

Fill  the  space  in  each  sentence  with  this  sign.  Read  the 
expressions. 

Finish  these  sentences : 

2+4  5+4  2+7 
5+2  4+2  3+5 
4+3  3+4  6+3 
7+2  8+2  2+8 
2+4        3+6        2+5 


Show  me  seven  fingers;  show  me  three  more  fingers. 
How  many  fingers  have  you  shown  me  altogether  ? 

It  sometimes  takes  a  week  and  three  days  to  go  across 
the  ocean.     How  many  days  does  it  take  ? 

In  a  class  at  school  there  were  seven  girls  and  three  boys. 
How  many  children  were  there  in  the  class? 


218  FIRST   STEPS   IN   NUMBER. 

I  bought  some  dress  goods  for  seven  dollars,  and  trim- 
mings for  the  dress  for  three  dollars.  How  much  did  the 
material  for  the  dress  cost  ? 

I  have  three  days  this  week  to  visit,  and  all  of  next  week. 
How  many  days  have  I  to  visit  ? 

Three  boys  are  playing  tag  and  seven  boys  are  playing 
ball.     How  many  boys  are  playing? 

In  our  little  duck-pond  there  are  three  old  ducks  and 
seven  ducklings.     How  many  are  there  in  all  ? 

Who  has  a  story  for  seven  and  three  ? 

Who  has  a  story  for  three  and  seven? 

If  I  have  seven  cents  and  a  three-cent  piece,  how  many 
cents  have  I  ?  If  I  give  you  the  three-cent  piece,  how 
many  cents  shall  I  have  ? 

If  you  have  a  three-cent  piece  and  John  has  a  ten-cent 
piece,  how  much  more  money  has  John  than  you  ? 

There  were  ten  chickens  in  one  brood  and  three  in 
another  brood.  How  many  more  chickens  were  in  one 
brood  than  in  the  other  ? 

Charley  had  ten  newspapers  to  sell.  How  many  had  he 
left  after  he  had  sold  three? 

There  were  ten  lambs  in  a  flock.  Three  lambs  were  sold. 
How  many  were  there  then  in  the  flock  ?  If  seven  lambs 
had  been  sold,  how  many  would  have  been  left  in  the  flock? 

A  ten-quart  can  has  seven  quarts  of  milk  in  it.  How 
much  more  milk  will  it  hold  ? 

I  bought  ten  yards  of  cloth,  and  have  used  seven  yards. 
How  much  cloth  remains  in  the  piece  ? 

A  man  bought  ten  pounds  of  sugar,  but  seven  pounds  of 
the  sugar  spilled  out  on  his  way  home.  How  many  pounds 
had  he  when  he  reached  home  ? 

There  were  ten  frosted  cakes  on  the  table  at  tea.  After 
each  of  seven  children  had  eaten  one  cake,  how  many 
cakes  remained  ? 


THE   NUMBER  TEN.  219 

Who  has  a  story  for  ten  minus  three  ? 

Who  has  a  story  for  ten  minus  seven  ? 

If  a  bag  of  peanuts  cost  seven  cents,  how  many  bags  of 
peanuts  can  be  bought  for  ten  cents,  and  how  many  cents 
will  be  left  toward  buying  another  bag  ? 

How  many  quarts  of  berries,  at  eight  cents  a  quart,  can 
be  bought  for  ten  cents,  and  how  many  cents  will  be  left  ? 

How  many  dozen  pens,  at  nine  cents  a  dozen,  can  be 
bought  for  ten  cents  ? 

How  many  cents  will  be  left  after  buying  the  dozen 
pens? 


Take  six  blocks.  Find  how  many  more  you  must  take 
to  have  ten  blocks.  Six  blocks  and  four  blocks  are  how 
many  blocks? 

There  were  six  white  pins  on  a  cushion  and  four  black 
pins.     How  many  pins  were  on  the  cushion  ? 

It  is  six  miles  to  the  foot  of  the  mountain,  and  four  miles 
farther  to  the  lake.     How  far  is  it  to  the  lake  ? 

Two  triangles  and  a  square  have  how  many  sides  alto- 
gether ? 

If  you  have  two  three-cent  pieces  and  two  two-cent 
pieces,  how  much  money  have  you  ? 

It  will  take  a  farmer  a  week  and  four  days  to  finish  hay- 
ing.    How  many  days  will  it  take  him  to  finish  haying  ? 

On  our  street  are  four  elms  and  six  maples.  How  many 
trees  are  on  our  street? 

A  lady  painted  four  fans  this  week  and  six  last  week. 
How  many  fans  has  she  painted  altogether  ? 

In  a  cottage  there  are  four  rooms  upstairs  and  six  rooms 
downstairs.     How  many  rooms  are  in  the  cottage  ? 

Who  has  a  story  for  six  and  four  ? 

Who  has  a  story  for  four  and  six? 


220  FIEST  STEPS   IN  NUMBER. 

If  there  were  ten  persons  at  table,  and  four  of  these  were 
children,  how  many  grown  persons  were  there  at  table  ? 

There  were  ten  little  girls  looking  in  at  a  shop  window. 
Four  of  them  went  in  to  buy  something.  How  many  were 
then  looking  in  at  the  window  ? 

Jennie  has  ten  words  to  write.  How  many  will  she 
have  to  write  after  writing  four  words  ? 

I  can  see  ten  boats  on  the  pond.  Six  of  the  boats  have 
sails.     How  many  are  row-boats  ? 

If  you  have  ten  weeks'  vacation,  and  spend  six  weeks  of 
your  vacation  in  the  country,  how  many  weeks  will  remain 
in  your  vacation  ? 

If  a  stake  is  ten  inches  long,  and  six  inches  are  above 
ground,  how  many  inches  of  the  stake  are  in  the  ground  ? 

Who  has  a  story  for  ten  minus  four  ? 

Who  has  a  story  for  ten  minus  six  ? 

Finish  these  expressions : 


6  +  4  = 

10  minus  4  = 

4  +  6  = 

10  minus  6  = 

4  +   =10. 

10  minus 

=  4. 

6  +   =10. 

10  minus 

=  6. 

If  an  orange  cost  six  cents,  how  many  oranges  can  be 
bought  for  ten  cents  ?  How  many  cents  will  remain  after 
buying  the  orange  ? 

How  many  newspapers,  at  four  cents  a  paper,  can  be 
bought  for  ten  cents  ?  What  part  of  the  cost  of  a  paper 
will  remain  after  buying  the  two  papers  ? 


How  many  fingers  have  you  on  each  hand?  How  many 
have  you  on  both  hands  ? 

This  pansy  has  five  petals  and  this  pansy  has  five  petals. 
How  many  petals  have  both  pansies  ? 


THE   NUMBER  TEN.  221 

If  there  are  ^ve  red  morning-glories  and  five  white  ones 
on  our  vine,  how  many  morning-glories  are  on  our  vine? 

It  is  five  miles  to  Chestnut  Grove.  If  I  go  and  return, 
how  many  miles  do  I  travel  ? 

Janey  is  five  years  old  now.  How  old  will  she  be  five 
years  from  now  ? 

I  bought  a  book  for  five  cents  and  a  bottle  of  ink  for  five 
cents.     How  much  did  both  cost  ? 

Who  has  an  example  for  five  and  five  ? 

Make  five  straight  lines  on  the  board.  Cross  each  of 
these  lines.     How  many  lines  have  you  made  all  together  ? 

Express  on  the  board  :  5  +  5  =  10. 

Make  ten  dots  on  the  board.  Erase  five  dots.  How 
many  dots  remain  ? 

Who  has  a  story  for  ten  minus  five  ? 

In  a  garden  there  were  ten  varieties  of  roses.  During  a 
severe  winter  five  varieties  died.  How  many  varieties  of 
roses  were  then  in  the  garden  ? 

A  man  who  works  ten  hours  a  day  works  five  hours  be- 
fore dinner.     How  many  hours  does  he  work  after  dinner  ? 

If  you  have  ten  words  to  copy  and  copy  five  of  them, 
how  many  words  will  remain  to  be  copied  ? 

John  bought  two  toy  shovels  for  a  cent  apiece,  and  a  toy 
hammer  for  three  cents.  He  gave  a  ten-cent  piece  in  pay- 
ment.    How  much  money  ought  he  to  receive  in  change  ? 

Harry  earned  six  cents  one  week  and  four  cents  another 
week.  He  then  spent  five  cents.  How  many  cents  had  he 
left? 

Mary  visited  her  aunt  a  week  and  three  days  last  summer, 
and  it  rained  hard  five  days  while  she  was  there.  If  it  was 
pleasant  the  rest  of  the  time,  how  many  days  were  pleasant  ? 

One  hen  had  two  chickens  and  another  hen  had  eight 
chickens.  If  five  of  these  chickens  died,  how  many  chickens 
had  the  two  hens  together? 


222  FIRST  STEPS   IN   NUMBER. 

Express  on  the  board:  Ten  minus  five  are  five. 

Here  are  ten  blocks.  See  how  many  piles  you  can  make 
if  you  put  five  in  each  pile. 

If  a  boy  sells  apples  at  the  rate  of  five  for  a  cent,  how 
many  cents  will  he  get  for  ten  apples  ? 

If  a  horse  travels  five  miles  an  hour,  in  how  many  hours 
will  he  travel  ten  miles  ? 

How  many  five-cent  stamps  can  be  bought  for  ten  cents  ? 
how  many  five-cent  pencils  ?  how  many  dozen  elastic  bands 
at  five  cents  a  dozen  ? 

Each  think  of  a  story  for  ten  divided  by  five. 

"Write  on  the  board:  Ten  divided  by  five  are  two. 

Here  are  two  piles  of  blocks  with  five  blocks  in  each  pile. 
How  many  blocks  are  here  ?  how  many  fives  ? 

Here  are  two  strings  of  buttons  with  five  buttons  on  each 
string.  How  many  buttons  are  on  both  strings  ?  how  many 
fives? 

Show  me  two  hands.  How  many  fingers  on  each  hand  ? 
how  many  fingers  on  both  hands?  how  many  fives? 

If  you  had  five  cents  in  each  hand,  how  many  cents 
would  you  have  in  both  hands  ?  how  many  fives  ? 

Here  are  two  boxes  with  five  cents  in  each  box.  How 
many  cents  are  in  both  boxes  ?  how  many  fives  ? 

I  have  two  five-cent  pieces.     How  many  cents  have  I  ? 

If  I  buy  two  five-cent  books,  what  must  I  pay  for  both 
books  ?  * 

If  Ella  uses  five  cents'  worth  of  paper  each  day,  how 
many  cents'  worth  will  she  use  in  two  days  ? 

How  many  toes  has  a  cat  on  two  fore-feet  ? 

How  many  toes  has  a  dog  on  two  feet  ? 

How  many  petals  have  two  apple-blossoms  ? 

I  have  dye  dollars  in  my  purse.  I  wish  I  had  twice  as 
much  money  in  my  purse.  How  many  dollars  do  I  wish  I 
had  in  my  purse  ? 


THE   NUMBER   TEN.  223 

If  there  are  five  desks  in  a  row,  and  twice  as  many  chairs 
as  desks,  how  many  chairs  are  there  ? 

This  strip  of  paper  is  five  inches  wide,  and  twice  as  long 
as  it  is  wide.     How  long  is  this  strip  of  paper  ? 

I  can  walk  five  miles  without  feeling  tired.  Soon  I  hope 
to  walk  twice  as  far.     How  far  will  that  be  ? 

Two  fives  are  how  many  ? 

Twice  five  are  how  many  ? 

Write  :  2  fives  =  ten. 

Each  take  ten  sticks.  Show  me  one-half  of  the  number 
of  sticks  you  have.     How  many  sticks  do  you  show  me? 

If  a  man  has  ten  cows,  and  sells  half  of  what  he  has, 
how  many  cows  does  he  sell  ? 

If  it  is  ten  miles  to  Boston,  how  far  is  it  half  way  there  ? 

I  can  ride  ten  miles  on  my  ticket.  If  I  use  half  of  my 
ticket,  how  many  miles  do  I  ride  ? 

I  divided  ten  pears  equally  between  two  boys.  How 
many  pears  did  I  give  to  each  ? 

I  have  ten  cents.  If  I  spend  five  cents,  what  part  of  my 
money  do  I  spend  ? 

Nettie  had  ten  nuts.  She  gave  me  five.  What  part  of 
her  nuts  did  she  give  me  ? 

Annie  has  ten  paper  dolls.  Sarah  has  none.  How  many 
dolls  must  Annie  give  Sarah  that  each  may  have  as  many 
as  the  other  ? 

Edwin  has  ten  lozenges  which  he  is  going  to  give  to  John 
and  Henry.  If  he  gives  to  each  the  same  number,  how 
many  will  John  have  ? 

If  a  milliner  puts  ten  yards  of  ribbon  on  two  hats,  so  that 
there  is  just  as  much  ribbon  on  one  hat  as  on  the  other, 
how  many  yards  does  she  put  on  each  hat? 

Who  thinks  of  a  story  for  one-half  of  ten  ? 

What  is  one-half  of  ten  ? 

Write  :  |  of  10  -  5. 


224  FIRST  STEPS   IN   NUMBER. 


The  Sign  — . 

Who  knows  what  word  I  have  omitted  in  each  of  these 
expressions  ? 

6  1-6.  6  3  =  3. 

10  1-^9.  4  2  =  2. 

10  5  =  5.  2  1  =  1. 

8  4  =  4.  7  1  =  6. 

Read  the  first  expression,  supplying  the  word  that  is 
needed.  (Let  teacher  make  the  sign  — -  instead  of  writing 
the  word.) 

Eead  the  second  expression.  (Let  teacher  make  the 
sign-.) 

Read  the  next  expression ;  the  next ;  the  next.  (Each 
time  the  expression  is  read,  let  the  teacher  make  the  minus 
sign.  When  the  sign  has  been  supplied  in  all  expressions, 
have  the  expressions  read  again.) 

Read  what  I  have  written : 

10  -  6  =  4.  10  -  2  =  8. 

10  -  7  =  3.  9  _  5  =.  4. 

10  -  8  =  2.  9-3  =  6. 

10  -  4  =  6.  9-7  =  2. 

10  -  3  =  7.  9-4  =  5. 


Write : 


Eight  minus  four  are  four. 
Seven  minus  four  are  three. 
Six  minus  four  are  two. 
Nine  minus  four  are  five. 
Ten  minus  four  are  six. 
Ten  minus  seven  are  three. 
Ten  minus  six  are  four. 


THE   NUMBER   TEN.  225 

Finish  these  statements  that  I  have  begun : 

10-4=  8-3  = 

10-6=  8-5  = 

10  -  1  =  7  -  5  = 

10-5=  7-2  = 

7-3=  8-7= 

7-4=  9-7= 

Exercise  for  Review. 

There  were  ten  little  soldiers  marching  very  straight. 
Two  fell  out  of  the  line,  and  then  how  many  were  in  line  ? 

There  were  ten  pins  standing  firm  and  even.  I  threw  a 
ball  and  knocked  down  seven.  How  many  were  left 
standing  ? 

We  will  call  our  fingers  fairies.  If  three  are  ugly  fairies, 
how  many  are  good  fairies  ? 

Each  of  these  fairies  has  a  cap.     If  half  have  pink  caps, 
and  the  rest  black  caps,  how  many  have  black  caps  ? 
.  Two  of  these  fairies  are  clumsy  and  thick.     How  many 
are  slender? 

Each  of  the  thick  fairies  has  two  joints.  How  many 
joints  have  both?  Each  of  the  others  has  three  joints. 
How  many  joints  have  three  of  the  others? 

Each  boy  has  two  ears,  two  cheeks,  two  eyes,  a  forehead 
and  a  nose,  a  mouth  and  a  chin.  How  many  parts  has  each 
boy's  head  ? 

If  each  arm  has  a  hand,  a  wrist,  a  forearm,  an  elbow, 
and  an  upper  arm,  how  many  parts  has  each  arm  ?  How 
many  parts  have  both  arms  ? 

If  each  tooth  has  a  crown,  a  neck,  and  a  root,  how  many 
parts  has  each  tooth  ?     How  many  parts  have  two  teeth  ? 

A  horse  has  one  toe  on  each  foot.  How  many  more  toes 
have  you  than  a  horse  ? 


226  FIRST  STEPS   IN   NUMBER. 

An  ox  has  two  toes  on  each  foot.  How  many  more  toes 
have  you  than  an  ox?  How  many  more  toes  has  an  ox 
than  a  horse  ? 

An  ox  wears  a  shoe  on  each  toe.  How  many  more  shoes 
does  an  ox  wear  than  you  ? 

A  hen  has  four  toes  on  each  foot.  How  many  toes  has 
she  on  both  feet? 

If  one  bird  has  no  teeth,  how  many  teeth  have  ten  birds  ? 

Each  feather  has  a  stem  and  a  vane.  How  many  stems 
and  vanes  together  have  three  feathers  ?  have  four  feathers  ? 
have  five  feathers  ? 

A  squirrel  has  four  toes  on  each  fore-foot,  and  ^ve  toes  on 
each  hind-foot.  How  many  toes  has  he  on  one  fore-foot  and 
one  hind-foot.  How  many  toes  has  he  on  his  fore-feet? 
How  many  toes  on  his  hind-feet  ? 

A  frog  has  four  toes  on  each  fore-foot,  and  five  toes  on 
each  hind-foot.  How  many  toes  has  a  frog  on  one  fore-foot 
and  hind-foot  together  ?  How  many  toes  has  a  frog  on  his 
hind-feet? 

A  grasshopper  has  three  pairs  of  legs  and  two  pairs  of 
wings.  How  many  legs  and  wings  has  a  grasshopper, 
counted  together  ? 

If  one  insect  has  three  eyes  in  his  forehead,  how  many 
eyes  will  three  such  insects  have  in  their  foreheads  ? 

If  a  hen  has  four  eyelids  to  each  eye,  how  many  eyelids 
has  a  hen  ? 

If  a  spider  has  four  pairs  of  legs,  how  many  legs  has  a 
spider  ? 

Write  on  the  board  the  figures  that  stand  for  the  num- 
bers I  show  you.  (In  this  way  test  the  child's  knowledge 
of  figures.) 

Read  what  I  show  you  with  the  blocks,  then  express 
what  you  read.  (The  sign  for  multiplication  and  the  sign 
for  division  have  not  yet  been  given.) 


THE   NUMBER  TEN.  227 

Who  has  an  example  for  what  I  have  expressed  on  the 


board? 

6  +  4  =  10. 

9  divided  by  3  ^ 

=  3. 

5  +  3=    8. 

8  divided  by  2 

=  4. 

7  +  3  =  10. 

10  divided  by  5 

=  2. 

5  +  4=   9. 

10  divided  by  2 

=  5. 

9-6=   3. 

2  fives  =10. 

10-4=    6. 

5  twos  =  10. 

10-7=    3. 

10  zeros  =    0. 

10-6=  4. 

ioflO=    5. 

10-3=    7. 

|of   9=   3. 

10-8=   2. 

iof    8=2. 

10  -  0  =  10. 

iof   8=    1. 

Use  the  proper  signs  where  I  have  omitted  them: 

6        4         10.  10         7        3. 

10        6  4.  10        0      10. 

10        4  6.  10      10        0. 

4        6        10.  10        3        7. 


CHAPTER  XI. 

THE    NUMBER    ELEVEN. 


§  33.     The  Number  Eleven. 

Take  ten  splints.  Make  them  into  a  little  bundle,  and 
put  an  elastic  band  about  them.  Take  one  more  splint. 
How  many  splints  have  you  in  the  bundle  ?  How  many 
splints  besides  ?  Tell  me  what  you  have.  (Ten  and  one.) 
Who  knows  how  many  splints  ten  splints  and  one  splint 
are? 

Put  back  your  eleven  splints.  Take  eleven  again  the 
quickest  way  you  can.     (One  ten  and  one.) 

How  many  in  the  bundle?  how  many  besides?  One  ten 
and  one  are  how  many  ?  Write  in  words  :  One  ten  and 
one  are  eleven. 

Who  can  express  the  number  eleven  in  figures? 

Who  knows  what  the  two  ones  mean  ? 

Show  me  the  one  that  stands  for  one  ten.  The  one  that 
stands  for  one. 


Take  nine  blocks.  Take  two  more  blocks.  How  many 
blocks  have  you  ?     Who  has  an  example  for  nine  and  two  ? 

I  have  three  three-cent  pieces,  and  a  two-cent  piece  of 
money.     How  much  money  have  I  ? 

If  I  bought  three  three-cent  stamps  and  a  two-cent 
stamp,  how  much  money  did  I  spend  ? 

If  you  buy  three  three-cent  pencils  and  one  two-cent 
pencil,  how  much  money  must  you  give  for  them  ? 


THE   NUMBER   ELEVEN.  229 

If  you  have  two  cents,  and  earn  nine  more  cents,  how 
many  cents  will  you  then  have  ? 

There  are  two  blossoms  and  nine  buds  on  our  night- 
blooming  plant.  How  many  buds  and  blossoms  are  on  the 
plant  ? 

There  are  two  peach  trees  and  nine  pear  trees  in  our 
garden.  How  many  trees  are  in  the  garden  ?  If  the  two 
peach  trees  die,  how  many  trees  will  remain  ? 

If  you  put  back  4iwo  of  the  eleven  blocks  you  have  shown 
me,  how  many  blocks  will  you  show  me  ? 

Eepresent  eleven  trees  on  the  board,  two  of  them  lying 
on  the  ground.     How  many  are  standing? 

Eepresent  eleven  chimneys.  Two  have  no  smoke  coming 
out  of  them  ;  the  rest  have.  From  how  many  chimneys  is 
the  smoke  coming? 

Eepresent  eleven  frogs,  two  on  the  edge  of  the  pond,  and 
the  others  in  the  pond.     How  many  are  in  the  pond  ? 

Illustrate  these  stories : 

Eleven  blackbirds  were  flying  in  the  air,  but  nine  alighted 
on  the  ground. 

Eleven  clay  balls  were  drying  in  the  sun.  Nine  cracked 
in  drying. 

Eleven  lamp-posts  are  on  the  street.  Only  nine  have 
lamps  on  them. 

I  have  eleven  lead-pencils.  Nine  of  them  are  sharpened, 
and  the  rest  are  not. 

Eleven  umbrellas  stood  in  a  shop  window.  Nine  were 
shut  and  the  rest  were  open. 

Write  on  the  board : 

Nine  and  two  are  eleven. 
Two  and  nine  are  eleven. 
Eleven  minus  two  are  nine. 
Eleven  minus  nine  are  two. 
Ten  and  one  are  eleven. 


230  FIRST  STEPS   IN   NUMBER. 

Complete  these  expressions : 


9+2  = 

10 

1         11. 

11-2  = 

11- 

=  10. 

2+    9  = 

11 

0        11. 

11-9  = 

11  - 

=    9. 

11-10  = 

11  ones      = 

11  zeros  = 

11  divided  by  1 

9+       = 

11. 

9 

2        11. 

11-       = 

9. 

11 

2          9. 

2+       = 

11. 

2 

9        11. 

11-       = 

2. 

11 

9          2. 

There  were  eight  tin  pans  and  three  milk-pails  on  a 
bench  drying  in  the  sun.  Show  me,  with  the  splints,  how 
many  things  were  on  the  bench. 

Eight  hens  and  three  worms  are  how  many  things? 

Eight  men  and  three  boys  are  how  many  persons  ? 

Eight  chickens  and  three  ducks  are  how  many  fowls? 

Eight  sky-rockets  and  three  flying  pigs  are  how  many 
pieces  of  fireworks  ? 

Tell  me  about  eight  bunches  of  grapes  and  three  bunches 
of  grapes ;  eight  pears  and  three  pears  ;  eight  great  apples 
you  saw  at  the  fair  and  three  small  apples ;  eight  red  bal- 
loons and  three  blue  balloons. 

If  you  spent  four  two-cent  pieces  and  a  three-cent  piece 
for  molasses  candy,  how  much  did  you  spend  ? 

How  many  legs  have  two  dogs,  and  a  stool  with  three 
legs? 

If  a  blacksmith  shoes  two  horses  entirely  round,  and  puts 
three  shoes  on  another  horse,  how  many  shoes  does  he  use  ? 

If  I  have  four  pairs  of  shoes,  and  three  odd  shoes,  how 
many  shoes  have  I  ? 


THE   NUMBER   ELEVEN.  231 

I  have  a  five-cent  piece  of  money,  a  three-cent  piece,  and 
three  one-cent  pieces.     How  much  money  have  I? 

There  are  three  boys  and  eight  girls  in  the  first  class, 
and  eight  boys  and  three  girls  in  the  second  class.  Which 
is  the  larger  class  ? 

Mr.  Brown  has  eight  cows  and  three  horses.  Mr.  Smith 
has  three  cows  and  eight  horses.  "Which  has  the  more 
animals  ? 

Which  costs  the  more :  some  candy  for  three  cents  and  a 
pencil  for  eight  cents,  or  some  candy  for  eight  cents  and  a 
pencil  for  three  cents  ? 

If  I  have  four  two-cent  pieces  of  money  and  a  three-cent 
piece,  and  spend  the  three-cent  piece,  how  much  money  shall 
I  have  left? 

If  eleven  dor-bugs  should  come  in  at  my  window,  and 
three  should  alight  on  my  table,  how  many  more  dor-bugs 
would  still  be  flying  about  the  room  ? 

If  eleven  ants  were  carrying  away  a  great  beetle,  and 
three  got  tired  and  ran  away,  how  many  ants  were  left  to 
carry  the  beetle  ? 

If  eleven  flies  were  sipping  at  a  drop  of  molasses,  and 
three  flew  away,  how  many  flies  were  there  sipping  at  the 
molasses  ? 

Make  some  drawing  on  the  board  to  show  me  that  eleven 
minus  three  are  eight. 

Does  any  one  know  what  eleven  minus  eight  are  ? 

Who  has  a  story  for  eleven  minus  eight  ? 

If  eleven  nuts  minus  eight  nuts  leave  three  nuts,  what 
will  be  left  if  three  nuts  are  taken  from  eleven  nuts  ? 

If  eleven  blocks  minus  three  blocks  leave  eight  blocks, 
what  number  will  eleven  minus  eight  leave  ? 

Write  :         Eight  and  three  are  eleven. 

Eleven  minus  three  are  eight. 
Eleven  minus  eight  are  three. 


232  FIRST   STEPS   IN   NUMBER. 

Complete  these  expressions : 

11-3  = 

8  +  3  = 
11-8- 

3  +  8  = 

9  +  2  = 
11-2  = 

2  +  9  = 
11-9  = 
11-     =8. 

8+     =11. 
11  -     =3. 

3+     =11. 


11 

3 

8. 

8 

8 

11. 

11 

8 

3. 

3 

8 

11. 

9 

2 

11. 

11 

2 

9. 

2 

9 

11. 

11 

9 

2. 

9  + 

=  11. 

11- 

=    9. 

2  + 

=  11. 

11- 

=    2. 

Nellie,  stand  seven  spools  in  a  row.  Put  four  more 
spools  with  them.     How  many  spools  are  now  in  the  row? 

Frank,  set  out  seven  tin  plates ;  set  out  four  more.  How 
many  tin  plates  have  you  set  out  altogether? 

Seven  horses  and  four  sheep  are  how  mauy  animals  ? 

A  pound  of  flour  at  seven  cents,  and  a  pound  of  meal  at 
four  cents,  will  cost  how  much  ? 

The  cook  made  seven  loaves  of  bread  and  four  loaves 
of  cake.  How  many  loaves  of  bread  and  cake  together  did 
she  make  ? 

A  week  and  four  days  are  how  many  days  ? 

A  five-cent  piece,  a  two-cent  piece,  and  four  cents  are 
how  many  cents? 

During  three  weeks,  Annie  went  to  school  one  whole 
week,  two  days  another  week,  and  four  days  the  other 
week.  How  many  days  did  she  go  to  school  during  the 
three  weeks? 

If  seven  and  four  are  eleven,  four  and  seven  are  how 
many? 


THE   NUMBER   ELEVEN.  233 

"Which  are  more  chickens:  seven  black  chickens  and 
four  white  ones,  or  four  black  chickens  and  seven  white 
ones?  seven  gray  rabbits  and  four  white  rabbits,  or  four 
gray  rabbits  and  seven  white  ones  ?  seven  blue  ribbons  and 
four  red  ribbons,  or  four  blue  ribbons  and  seven  red  ones  ? 

Who  has  a  story  for  seven  and  four,  or  for  four  and 
seven  ?  

If  seven  and  four  are  eleven,  who  thinks  how  many  eleven 
minus  four  will  leave  ?     See  if  you  are  right. 

Eleven  chairs  minus  four  chairs  are  how  many  chairs  ? 

Eleven  oranges  minus  four  oranges  are  how  many  oranges? 

Eleven  cents  minus  two  two-cent  pieces  are  how  many 
cents  ? 

Eleven  days  minus  four  days  will  leave  what  part  of  a 
week? 

Eleven  weeks  minus  a  month  will  leave  how  many 
weeks  ? 

Eleven  months  minus  four  months  will  leave  how  many 
months  ? 

Eleven  gills  of  milk  minus  a  pint  of  milk  will  leave  how 
many  gills  of  milk  ?  how  many  pints  of  milk  ? 

If  eleven  blocks  minus  four  blocks  leave  seven  blocks, 
who  thinks  how  many  blocks  would  remain  if  I  took  seven 
blocks  from  eleven  blocks.  See  if  you  are  right.  Who  has 
an  example  for  eleven  minus  seven  ? 

There  are  eleven  more  days  in  this  month.  How  many 
days  over  a  week  are  there  left  in  the  month  ? 

If  there  are  eleven  gills  of  water  in  this  pail,  and  I  dip 
out  seven  gills  of  water,  what  part  of  a  pint  will  remain  in 
the  pail  ? 

If  I  owe  you  eleven  cents,  and  pay  you  seven  cents,  then 
give  you  the  rest  in  two-cent  pieces,  how  many  two-cent 
pieces  shall  I  give  you  ? 


234  FIRST  STEPS   IN   NUMBER. 


Express  :      Seven  and  four  are 

eleven. 

Four  and  seven  are 

1  eleven. 

Eleven  minus  four 

are  seven. 

Eleven  minus  seven  are  four. 

Fill  out  these  expressions : 

7  +  4  = 

7 

4 

11. 

11-7  = 

11 

7 

4. 

11-4  = 

11 

4 

7. 

4+7  = 

4 

7 

11. 

11-8  = 

11 

8 

3. 

3  +  8  = 

3 

8 

11. 

11-3  = 

11 

3 

8. 

8  +  3  = 

8 

3 

11. 

9  +  2  = 

9 

2 

11. 

11-2  = 

11 

2 

9. 

11-9  = 

11 

9 

2. 

2  +  9  = 

2 

9 

11. 

7+     = 

11  - 

-     = 

:       4. 

8+     = 

11- 

-     =- 

:       3. 

9+     = 

11- 

-          -: 

:       2. 

4+     = 

11- 

= 

:       9. 

3+     = 

11- 

= 

:       8. 

2+     = 

11- 

= 

:       7. 

Draw  six  lines  up  and  down,  and  five  lines  from  right  to 
left.     How  many  lines  have  you  drawn  ? 

Draw  six  pans  right  side  up,  and  five  bottom  side  up. 
How  many  pans  have  you  drawn  ? 

Draw  six  flower-pots  with  saucers,  and  five  without 
saucers.     How  many  flower-pots  have  you  drawn  ? 

Draw  six  hassocks  and  ^ye  crickets.  How  many  foot- 
stools have  you  drawn  ? 


THE   NUMBER   ELEVEN.  235 

Show  me  six  sticks  of  one  color,  and  five  sticks  of  an- 
other color.     How  many  sticks  have  you  shown  me  ? 

Two  three-cent  pieces  of  money  and  a  five-cent  piece  are 
how  many  cents? 

Three  two-cent  pieces  of  money  and  a  five-cent  piece  are 
how  much  money  ? 

Who  has  seen  six  clothes-pins  and  five  handkerchiefs  on 
the  line  ? 

How  many  things  were  on  the  line  ? 

Tell  me  a  story  for  six  and  five. 

If  six  and  five  are  eleven,  how  many  are  five  and  six? 

Tell  me  a  story  for  five  and  six. 

If  you  have  six  peanuts  and  five  chestnuts,  how  many 
nuts  have  you  ? 

If  you  eat  the  five  chestnuts,  how  many  nuts  will  you 
have? 

If  you  have  eleven  walnuts,  and  eat  five  of  them,  how 
many  nuts  have  you  left  ? 

If  you  have  eleven  cents,  and  one  of  the  pieces  of  money 
is  a  five-cent  piece,  and  the  rest  is  in  cents,  how  many 
cent-pieces  have  you  ? 

If  there  are  eleven  beautiful  great  soap-bubbles  floating 
in  the  air,  and  five  burst,  how  many  remain  ?  If  six  had 
burst,  how  many  would  have  remained  ? 

I  can  buy  a  knife  for  eleven  cents.  If  I  pay  for  it  with 
a  five-cent  piece  and  one-cent  pieces  of  money,  how  many 
one-cent  pieces  do  I  pay  out  ?  If  I  paid  for  it  with  two 
three-cent  pieces  and  one-cent  pieces,  how  many  one-cent 
pieces  did  I  pay  out? 

In  the  school-yard  are  eleven  shade  trees.  Six  are  pop- 
lar trees,  and  the  rest  are  elm,  maple,  and  butternut.  How 
many  are  not  poplars  ? 

I  bought  eleven  yards  of  black  lace.  I  put  three  yards 
on  each  of  two  parasols.     How  many  yards  had  I  left  ? 


236  FIRST  STEPS   IN   NUMBER. 

Express :  Six  and  five  are  eleven. 

Five  and  six  are  eleven. 

Eleven  minus  ^ye  are  six. 

Eleven  minus  six  are  five. 
Fill  out  these  expressions : 


11-5  = 

11 

5 

6. 

6  +  5  = 

6 

5 

11. 

11-6  = 

11 

6 

5, 

5  +  6  = 

5 

6 

11. 

11-4  = 

11 

4 

7. 

7  +  4  = 

7 

4 

11. 

11-7  = 

11 

7 

4. 

4  +  7  = 

4 

7 

11. 

11-3  = 

11 

3 

8. 

8  +  3  = 

8 

3 

11. 

11-8  = 

11 

8 

3. 

3  +  8  = 

3 

8 

11. 

11-2  = 

11 

2 

9. 

9  +  2  = 

9 

2 

11. 

11-9  = 

11 

9 

2. 

2  +  9  = 

2 

9 

11. 

6+     = 

11- 

=    9. 

7+     = 

11- 

=    8. 

8+     = 

11- 

=    7. 

9+     = 

11- 

=    6. 

11+     = 

11- 

=    5. 

11-     = 

4. 

11- 

=    3. 

11-     = 

2. 

11- 

=    0. 

11+     = 

11. 

11- 

=  11. 

Exercise 

for  Review. 

Two  squares  and  a  triangle  have  how  many  sides  ? 
Two  triangles  and  a  square  have  how  many  sides  ? 


THE   NUMBER   ELEVEN.  237 

Three  triangles  have  how  many  sides  ? 

Two  squares  have  how  many  corners  ? 

A  square  and  a  triangle  have  how  many  corners  ? 

Two  triangles  have  how  many  corners  ? 

Eleven  geese  have  how  many  bills  ? 

I  saw  five  oxen  with  a  ball  on  each  horn.  How  many 
balls  did  it  take  for  all  the  oxen  ? 

My  lamp  has  two  shades,  a  glass  shade  and  a  porcelain 
shade.     How  many  shades  will  it  take  for  five  such  lamps  ? 

Five  rocking-chairs  have  how  many  rockers  ? 

A  cabinet-maker  made  two  chests,  with  five  drawers  in 
each  chest.  How  many  drawers  did  he  make  for  both 
chests  ? 

How  many  school-days  are  there  in  two  weeks  ? 

An  extension  table  has  five  legs.  How  many  legs  have 
two  extension  tables? 

How  many  leaves  has  one  sheet  of  paper  ?  How  many 
leaves  have  five  sheets  of  paper  ? 

Five  sheets  of  paper  and  a  half  sheet  are  how  many  half 
sheets  of  paper  ? 

A  week  and  four  days  are  how  many  days  ? 

A  month  and  seven  weeks  are  how  many  weeks  ? 

Two  pints  and  three  gills  are  how  many  gills  ? 

How  many  legs  and  wings,  together,  has  a  butterfly  ? 

A  week  and  three  days  are  how  many  days  ? 

Two  months  and  a  half  are  how  many  weeks  ? 

Two  pints  and  a  half  are  how  many  gills  ? 

This  line  is  ten  inches  long.     How  long  is  half  the  line  ? 

It  is  ten  miles  to  the  Falls.    How  far  is  it  half-way  there  ? 

I  can  buy  slate-pencils  at  two  for  a  cent.  How  many 
cents  will  ten  slate-pencils  cost  ? 

How  many  five-cent  stamps  can  I  buy  for  ten  cents? 
How  many  two-cent  stamps?  How  many  three-cent 
stamps  ?     How  many  one-cent  stamps  ? 


238  FIRST  STEPS   IN   NUMBER. 

If  lemons  are  five  cents  apiece,  how  many  can  I  buy  for 
ten  cents  ? 

How  many  five-cent  pieces  does  it  take  to  equal  ten 
cents  ? 

I  have  eleven  cents  in  two  pieces  of  money.  What  must 
the  pieces  of  money  be  ? 

I  have  eleven  cents  in  three  pieces  of  money.  What 
may  the  three  pieces  of  money  be  ?   What  else  may  they  be  ? 

I  have  eleven  cents  in  four  pieces  of  money.  What  may 
the  four  pieces  of  money  be?  What  else  may  they  be? 
What  else  may  they  be  ? 

Two  three-cent  pieces  and  a  five-cent  piece  of  money 
equal  how  many  cents? 

A  five-sided  figure  and  a  six-sided  figure  have  how  many 
sides  all  together? 

Eleven  chickens  have  gone  to  roost.  Six  are  roosting  in 
a  tree,  and  the  rest  on  a  fence.  How  many  are  roosting  on 
the  fence  ? 

There  are  eleven  children  in  my  third  class,  but  five  of 
them  got  so  tired  at  the  Fair  that  they  could  not  come  to 
school  to-day.     How  many  are  here  ? 

How  many  one-cent  pencils  can  you  buy  for  eleven  cents  ? 
How  many  two-cent  pencils  ?  How  many  three-cent  pen- 
cils ?  How  many  four-cent  pencils  ?  How  many  five-cent 
bunches  of  envelopes  ?  How  many  six-cent  quires  of  paper  ? 
How  many  seven-cent  books?  How  many  eight-cent 
slates  ?  How  many  bottles  of  ink  at  nine  cents  a  bottle  ? 
How  many  ten-cent  watches? 

Tell  me  any  two  numbers  that  together  make  eleven. 

Who  has  some  question  for  the  class  to  answer  ? 


CHAPTER  XII. 

THE    NUMBER    TWELVE. 


§  34.   The  Number  Twelve. 

Take  ten  splints.  Put  them  together  in  a  bundle,  and 
put  an  elastic  band  about  the  bundle.  Take  two  more 
splints.  How  many  splints  are  in  the  bundle?  How 
many  splints  have  you  besides?  Who  knows  how  many 
splints  ten  and  two  are  ? 

Put  back  the  twelve  splints.  Take  twelve  again  the 
quickest  way.     What  did  you  take  ?     (One  ten  and  two.) 

Write  in  words :  One  ten  and  two  are  twelve. 

Who  can  express  the  number  twelve  in  figures  ? 

How  many  figures  do  you  use  to  express  twelve?  What 
are  the  figures  ?  Which  figure  do  you  make  first  in  writing 
twelve  ?  Who  thinks  what  the  figure  1  stands  for  ?  What 
does  the  figure  2  stand  for  ?  One  ten  and  two  are  how 
many  ? 

Express  the  number  eleven  under  twelve.  Express  the 
number  ten  in  the  same  column.  How  many  ones  in  twelve 
besides  the  one  ten  ?  Point  to  the  figure  that  stands  for  the 
two  ones.  How  many  ones  in  eleven  besides  the  one  ten  ? 
Point  to  the  figure  that  stands  for  the  one.  How  many 
ones  in  ten  besides  the  ten  ones  ?  Point  to  the  figure  that 
shows  there  are  no  ones. 

If  you  have  been  to  school  two  weeks  and  two  days  this 
term,  how  many  days  have  you  been  to  school  ? 


240  FIRST  STEPS   IN   NUMBER. 

If  there  are  ten  great  yellow  cucumbers  cut  into  Jack-o- 
Lanterns,  and  two  more  waiting  to  be  cut  into  Jack-o- 
Lanterns,  bow  many  cucumbers  are  there  all  together  ? 

Rose  is  ten  years  old.  Her  brother  is  two  years  older. 
How  old  is  her  brother  ? 

If  there  are  ten  boys  playing  Fox  and  Geese,  and  two 
more  boys  join  them,  how  many  boys  are  playing  Fox  and 
Geese  ? 

There  are  ten  rooms  in  our  house  besides  the  two  attic 
rooms.     How  many  rooms  are  there  with  the  attic  rooms  ? 

Who  will  ask  me  a  question  about  ten  and  two  ?  Frank, 
ask  Charley  a  question  about  ten  and  two.  Nellie,  ask 
Mary  a  question  about  ten  and  two. 

Ten  apple  turnovers  and  two  apple  turnovers  are  how 
many? 

Ten  beautiful  girl-dolls  and  two  soldier-dolls  are  how 
many  dolls? 

If  ten  and  two  are  twelve,  two  and  ten  are  how  many? 

Two  jugs  and  ten  pitchers  are  how  many  things? 

Two  saucers  and  ten  butter-plates  are  how  many  dishes? 

Two  knives  and  ten  forks  are  how  many  things  ? 

Two  children  in  the  middle  of  a  ring,  and  ten  in  the  ring 
make  how  many  children  ? 

If  the  two  that  are  in  the  middle  of  the  ring  run  away, 
how  many  will  be  left  ? 

If  twelve  girls  are  playing  Drop  the  Handkerchief,  and 
two  fall  out  of  the  ring,  how  many  are  left  ? 

If  twelve  boys  are  playing  King's  Land,  and  two  get 
caught,  how  many  will  be  left  to  play  ? 

There  are  twelve  working  days  in  two  weeks.  How 
many  working  days  are  there  in  two  weeks  minus  two 
days  ? 

Show  me  twelve  splints.  Take  away  ten  splints,  and 
tell  me  how  many  remain. 


THE  NUMBER  TWELVE.  241 

Tell  me  about  twelve  chimney  swallows,  and  two  came 
down  the  chimney  into  the  room.  About  twelve  eggs,  and 
two  were  used  for  cake.  About  twelve  months  in  the  year, 
and  you  were  away  visiting  two  months  in  the  year. 

If  you  have  twelve  cents,  and  spend  ten  cents,  how  many 
cents  will  you  have  ? 

If  I  have  twelve  postal  cards,  and  use  ten,  how  many 
postal  cards  shall  I  have  ? 

If  I  teach  ten  months  in  the  year,  how  many  months 
have  I  for  vacation  ? 

If  I  have  twelve  cents  in  two  pieces  of  money,  and  one 
of  the  pieces  of  money  is  a  ten-cent  piece,  what  is  the  other 
piece  of  money  ? 

There  were  ten  cows  and  a  pair  of  oxen  feeding  in  a 
pasture.     How  many  cattle  were  in  the  pasture  ? 

There  were  twelve  books  lying  on  my  table,  and  I  put 
all  but  two  on  the  book-case.  How  many  did  I  put  on  the 
book-case  ? 

It  will  take  two  yards  of  trimming  for  my  dress,  and  ten 
yards  of  dress  goods.  How  many  yards  of  material  must  I 
buy  for  my  dress  ? 

There  are  twelve  tacks  in  my  screen,  but  two  have  lost 
their  heads.     How  many  are  whole  ? 

Stand  twelve  spools  up  for  soldiers.  Make  them  march 
by  twos.     How  many  twos  are  there  in  the  twelve  ? 

Call  the  spools  gate  posts.  If  it  takes  two  for  each  gate, 
how  many  gates  can  you  supply  with  posts  ? 

Call  these  twelve  sticks  shafts  for  carriages.  For  how 
many  carriages  have  you  shafts  ?  Call  them  curtain  sticks. 
If  it  takes  two  for  each  curtain,  how  many  curtains  can 
you  supply? 

Call  them  sled  runners.  How  many  sleds  can  you  sup- 
ply with  runners  ? 

Tell  me  a  story  for  twelve  divided  by  two. 


242  FIRST  STEPS  IN   NUMBER. 

If  there  are  six  twos  in  twelve,  how  many  twos  make 
twelve  ? 

Six  boys  have  how  many  eyes?  how  many  ears?  how 
many  shoulders  ?  how  many  feet  ?  how  many  arms  ? 

Six  jackets  have  how  many  sleeves? 

Six  pairs  of  trousers  have  how  many  legs  ? 

Two  flies  have  six  times  as  many  legs  as  a  boy.     How 
many  legs  have  two  flies  ? 

Jennie  is  two  years  old,  and  Harry  is  six  times  as  old. 
How  old^  is  Harry  ? 

A  small  pail  holds  two  quarts.    The  water-pail  holds  six 
times  as  much.     How  much  does  the  water-pail  hold  ? 

I  will  give  you  another  name  for  twelve.     We  call  it  a 
dozen. 

A  dozen  eggs  are  how  many  eggs  ? 

A  dozen  baskets  of  wood  are  how  many  baskets  of  wood  ? 

A  dozen  fruit  cans  are  how  many  cans  ? 

A  dozen  persons  are  how  many  persons  ? 

A  dozen  peaches  are  how  many  peaches  ? 

Where  have  you  heard  the  word  dozen  before  ? 

Whenever  you  hear  the  word,  of  what  number  will  you 
think? 

How  many  pairs  of  boots  in  a  dozen  boots  ? 

If  you  buy  a  dozen  eggs,  and  use  two  eggs,  how  many 
eggs  have  you  left  ? 

If  you  use  ten  eggs,  how  many  eggs  have  you  left  ? 

If  the  family   eats  a  dozen  tomatoes  for  dinner,  how 
many  tomatoes  are  eaten  ? 

Express  :  Ten  and  two  are  twelve. 

Twelve  minus  two  are  ten. 
Twelve  minus  ten  are  two. 
Two  and  ten  are  twelve. 
Twelve  divided  by  two  are  six. 
Six  twos  are  twelve. 


THE   NUMBER  TWELVE.  243 


Fill  out  these  blanks : 

10+2  = 

10 

2         12. 

12-2  = 

12 

2         10. 

2+10  = 

2 

10         12. 

12  -  10  = 

12 

10          2. 

12-       = 

10. 

12  divided  by  2  = 

10+       = 

12. 

6  twos  = 

12-       = 

2. 

12  divided  by      =  6. 

2+       = 

12. 

6 

-12. 

A  farmer,  in  counting  his  eggs  for  the  market,  found  he 
had  ten  dozen  and  nine  more  eggs.  Who  can  find  how 
many  eggs  he  lacked  of  another  dozen  ? 

Nine  eggs  and  three  eggs  are  how  many  eggs? 

If  I  have  three  three-cent  pieces,  and  three  one-cent 
pieces  of  money,  how  much  money  have  I  ? 

Annie  had  nine  cents,  and  Nellie  had  a  three-cent  piece. 
How  much  money  had  both  ? 

If  you  begin  school  at  nine  in  the  morning,  and  are  in 
school  three  hours,  what  time  is  it  when  you  are  dismissed  ? 

If  Johnny  falls  asleep  at  nine  o'clock,  but  wakes  when 
the  clock  is  striking  twelve,  how  many  hours  has  he  been 
asleep  ? 

I  can  start  from  the  railroad  station  at  nine  in  the  morn- 
ing, and  get  to  Boston  at  noon.  How  many  hours'  ride  is 
it  to  Boston? 

James  bought  a  dozen  eggs  at  the  store,  but  tipped  three 
out  of  his  basket  on  the  way  home.  How  many  had  he 
when  he  reached  home  ? 

We  put  up  a  dozen  cans  of  peaches  one  fall,  but  gave 
away  three  cans.  How  many  cans  did  we  have  for  our 
own  use  ? 


244  FIRST   STEPS   IN   NUMBER. 

I  can  buy  little  boxes  of  pens  with  a  dozen  pens  in  each, 
box.  If  I  use  nine  out  of  a  box,  how  many  will  remain  in 
the  box? 

I  picked  a  dozen  quarts  of  berries,  and  sold  nine  quarts. 
How  many  quarts  did  I  keep  for  my  own  use? 

There  are  a  dozen  panes  of  glass  to  be  set  in  a  window. 
When  nine  are  set,  how  many  more  are  to  be  set? 

If  I  have  a  dozen  pencils  to  sharpen,  and  sharpen  nine 
of  them,  how  many  pencils  shall  I  still  have  to  sharpen  ? 

I  had  a  box  of  thread  with  a  dozen  spools  in  it,  but  have 
used  nine  spools.     How  many  spools  have  I  left? 

Who  can  tell  me  about  nine  tops  and  three  tops?  nine 
houses  and  three  barns?  nine  crows  and  three  scare-crows  ? 
nine  watermelons  and  three  green  pumpkins  ? 

Draw  three  tops  on  the  board  ;  draw  below  them  nine 
others.     How  many  tops  have  you  drawn  ? 

Draw  anything  you  choose  to  show  that  three  and  nine 
are  twelve. 

If  I  have  nine  peaches,  how  many  more  peaches  must  I 
have  to  make  a  dozen  peaches?  What  then  is  the  differ- 
ence between  nine  and  twelve? 

If  Susie  finds  a  dozen  pins,  and  Mary  finds  only  nine, 
how  many  more  pins  does  Susie  find  than  Mary  ? 

Some  kinds  of  candy  are  nine  cents  a  quarter,  and  other 
kinds  are  twelve  cents  a  quarter.  What  is  the  difference 
in  price? 

Some  lace  is  nine  cents  a  yard,  and  other  lace  is  twelve 
cents  a  yard.     What  is  the  difference  in  price? 

If  I  have  three  sheets  of  paper,  how  many  more  sheets 
of  paper  must  I  have  to  make  a  dozen  sheets  of  paper? 
What  then  is  the  difference  between  three  and  twelve  ? 

Who  knows  how  many  threes  there  are  in  twelve? 
Twelve  divided  by  three  are  how  many  ? 

How  many  boxes  will  it  take  for  twelve  dozen  eggs  if 
you  pack  three  dozen  eggs  in  each  box  ? 


THE   NUMBER  TWELVE.  245 

I  have  twelve  cents  in  three-cent  pieces.  How  many 
three-cent  pieces  have  I  ? 

How  many  three-cent  stamps  can  I  buy  for  twelve  cents  ? 
How  many  three-cent  pencils  ?  How  many  three-cent 
rubbers  ? 

How  many  three-quart  pails  will  it  take  to  hold  twelve 
quarts  of  cranberries  ? 

Who  will  tell  me  a  story  about  twelve  divided  by  three  ? 

Draw  twelve  bottles  on  the  board,  and  put  them  in  rows 
of  three  each.     How  many  rows  of  bottles  have  you  ? 

Four  rows  of  bottles,  with  three  in  each  row,  are  how 
many  bottles  ? 

If  a  dozen  buttons  are  arranged  on  a  card  in  rows  of 
three  each,  how  many  rows  of  buttons  are  there? 

Four  rows  of  buttons,  with  three  buttons  in  a  row,  are 
how  many  buttons  ? 

Four  velocipedes  have  how  many  wheels,  if  each  veloci- 
pede has  three  wheels  ? 

A  tricycle  has  three  wheels.  How  many  wheels  have  four 
tricycles  ? 

My  little  basket  watch-stand  has  three  legs.  How  many 
legs  will  four  such  watch-stands  have? 

Most  pitchforks  have  three  tines  each.  How  many  tines 
do  four  pitchforks  have  ? 

Four  horse-cars,  with  three  horses  attached  to  each  car, 
have  how  many  horses  ? 

Four  houses,  with  three  chimneys  each,  have  how  many 
chimneys? 

Tell  me  a  story  for  four  threes. 

Express :      Nine  and  three  are  twelve. 

Twelve  minus  three  are  nine. 
Three  and  nine  are  twelve. 
Twelve  minus  three  are  nine. 
Twelve  divided  by  three  are  four. 
Four  threes  are  twelve. 


246 


FIRST  STEPS   IN   NUMBER. 


Finish  these  expressions : 


12-3  = 

12 

3 

9. 

9+    3  = 

9 

3 

12. 

12-9  = 

12 

9 

3. 

3+    9  = 

3 

9 

12. 

12-2  = 

12 

2 

10. 

12  -  10  = 

12 

10 

2. 

10+2  = 

10 

2 

12. 

2  +  10  = 

2 

10 

12. 

6  twos  = 

12  divided 

by  2  = 

4  threes  = 

12  divided 

by  3  = 

12-       =9. 

9  + 

= 

12. 

12-       =3. 

3  + 

= 

12. 

12-       =2. 

2  + 

= 

12. 

lii'  -       =  10. 

10  + 

= 

12. 

6           =  12. 

12 

2  = 

6. 

4           =  12. 

12 

3  = 

4. 

If  I  cut  a  pie  into  four  equal  parts,  what  part  of  the  pie 
is  each  piece?  If  I  separate  a  number  into  four  equal 
groups,  what  part  of  the  number  is  each  group  ? 

You  may  separate  twelve  into  four  equal  groups.  What 
part  of  twelve  is  each  group?  Show  me  one-fourth  of 
twelve.     What  is  one-fourth  of  twelve  ? 

If  I  have  a  dozen  apples,  and  give  you  one-fourth  of  what 
I  have,  how  many  apples  shall  I  give  you? 

If  I  have  a  dozen  geranium  blossoms,  and  one-fourth  of 
them  drop  off,  how  many  blossoms  drop  off? 

If  I  use  a  quarter  of  a  dozen  eggs,  how  many  eggs  shall 
I  use? 

There  are  twelve  months  in  a  year.  One-fourth  of  the 
year  is  how  many  months  ?  Summer  is  one-fourth  of  the 
year.     How  long  is  Summer? 

Winter  is  one-fourth  of  the  year.  How  long  is  Winter  ? 
Each  of  our  seasons  is  one-fourth  of  the  year.  How  long  is 
each  season  ? 


THE   NUMBER   TWELVE.  247 

If  I  divide  twelve  chocolate  mice  equally  among  four 
little  girls,  how  many  chocolate  mice  shall  I  give  to  each  ? 

I  have  a  three-cent  piece  in  my  hand,  which  is  one-fourth 
of  all  the  money  I  have.     How  much  money  have  I  ? 

Ada  spent  three  weeks  in  the  country,  which  was  one- 
fourth  of  her  vacation.     How  long  was  her  vacation  ? 

John  was  absent  from  school  a  fourth  of  the  term.  He 
was  absent  three  weeks.     How  long  was  the  term  ? 

A  gentleman  received  three  letters  one  day,  which  was 
only  one-fourth  of  what  he  usually  received.  How  many 
did  he  usually  receive  ? 

Who  has  a  story  for  one-fourth  of  twelve  ? 

Express  this  fact  a  dozen  times  on  the  board  (^  of  12  is  3). 


Here  are  some  paper  patterns.  Each  take  eight  of  a 
kind.  What  have  you  taken,  Bessie  ?  (Butterflies.)  Take 
four  more  butterflies.  Harry  ?  (Horses.)  Take  four  more 
horses.  Nellie?  (Brooms.)  Take  four  more  brooms. 
John  ?  (Shovels.)  Take  four  more  shovels.  How  many 
butterflies  have  you,  Bessie  ?  Eight  butterflies  and  four 
butterflies  are  how  many  butterflies?  How  many  horses 
have  you,  Harry  ?  Eight  horses  and  four  horses  are  how 
many  horses  ?  How  many  brooms  have  you,  Nellie  ?  Eight 
brooms  and  four  brooms  are  how  many  brooms?  How 
many  shovels  have  you,  John?  Eight  shovels  and  four 
shovels  are  how  many  shovels  ? 

Each  write :  Eight  and  four  are  twelve,  a  dozen  times  on 
the  board. 

Let  the  eight  and  four  change  places,  and  read  the  ex- 
pression (Four  and  eight  are  twelve). 

Who  has  an  example  for  four  and  eight  ? 

I  agreed  to  dress  a  dozen  paper  dolls  for  the  Fair.  I 
have  dressed  eight  dolls.     How  many  more  must  I  dress  ? 


248  FIRST   STEPS   IN   NUMBER. 

Eight  and  how  many  more  are  twelve  ?  A  wheel,  then, 
that  has  only  eight  spokes  needs  how  many  more  spokes 
to  make  twelve  spokes  ? 

I  can  buy  a  dozen  sheets  of  tissue  paper  for  eight  cents. 
Silver  paper  costs  a  cent  a  sheet.  How  much  more  will  a 
dozen  sheets  of  silver  paper  cost  than  a  dozen  sheets  of 
tissue  paper  ? 

When  dates  are  eight  cents  a  pound,  and  figs  twelve 
cents  a  pound,  what  is  the  difference  in  price? 

Express  on  the  board  the  difference  between  twelve  and 
eight. 

Twelve  is  four  more  than  what  number  ? 

Eight  is  four  less  than  what  number  ? 

Twelve  is  eight  more  than  what  number? 

Four  is  eight  less  than  what  number  ? 

Draw  on  the  board  twelve  pins,  putting  four  pins  in  each 
row.     How  many  rows  have  you  ? 

A  gardener  has  twelve  plants  which  he  is  going  to  set 
out  in  clusters  of  four  each.  How  many  clusters  can  he 
make? 

Here  are  twelve  sticks  of  equal  length.  How  many  sep- 
arate squares  can  you  form  with  them  ? 

Twelve  horse-shoes  will  supply  how  many  horses  with 
shoes  if  they  need  shoeing  all  round  ? 

Twelve  dollars  will  pay  for  how  many  weeks'  board,  if 
you  pay  four  dollars  a  week? 

A  ten-cent  piece  and  a  two-cent  piece  will  buy  how  many 
oranges  at  four  cents  apiece  ? 

Who  can  express  this  fact  on  the  board  ?  (12  divided 
by  4  =  3.) 

Express  it  just  as  many  times  as  there  are  fours  in 
twelve  ? 

Here  are  three  horses.  How  many  legs  have  they 
altogether  ? 


THE   NUMBER   TWELVE.  249 

Here  are  three  table-forks,  and  each  fork  has  four  tines. 
How  many  tines  have  the  three  forks  together  ? 

Three  chairs  have  how  many  legs  ? 

Three  squares  have  how  many  sides?  have  how  many 
corners  ? 

One  sheet  of  note-paper  has  how  many  pages  ?  Three 
sheets  have  how  many  pages  ? 

If  I  embroider  a  flower  in  each  corner  of  a  square  table- 
cover,  how  many  flowers  must  I  embroider  in  three  such 
table-covers  ? 

Three  four-pound  weights  are  equal  to  how  many  pound 
weights  ? 

If  I  measure  three  pints  of  milk  with  a  gill  dipper,  how 
many  times  must  I  fill  the  dipper  ? 

Three  four-wheeled  carriages  have  how  many  wheels? 

Express  this  fact  on  the  board  (3  fours  =  12). 

You  may  divide  twelve  into  three  equal  groups.  What 
part  of  twelve  is  each  group  ?  Show  me  one-third  of 
twelve.  How  many  do  you  show  me  in  one-third  of 
twelve  ? 

If  snow  is  on  the  ground  one-third  of  the  year,  how  many 
months  is  snow  on  the  ground? 

Susie  had  a  dozen  paper  dolls,  but  a  third  of  them  got 
torn..    How  many  got  torn? 

A  man  who  had  a  dozen  balloons  to  sell,  sold  a  third  of 
them  to  one  boy.     How  many  did  the  boy  buy  ? 

A  carriage-maker  has  just  finished  a  dozen  wheels.  He 
will  use  a  third  of  them  for  one  carriage.  How  many 
wheels  will  he  use  for  that  carriage  ? 

A  cooper  who  has  a  dozen  cask-hoops  will  use  four  on  a 
cask.  What  part  of  the  number  of  hoops  he  has  will  he 
use  for  one  cask  ? 

I  have  four  cents,  which  is  one-third  enough  money  to 
buy  a  dozen  sugar  cookies.  How  much  are  the  cookies  a 
dozen  ? 


250 


FIRST  STEPS   IN   NUMBER. 


I  have  four  pencils.    What  part  of  a  dozen  pencils  have  I  ? 

Four  is  what  part  of  twelve  ? 

One-third  of  twelve  is  how  many  ? 

Give  me  an  example  for  one-third  of  twelve  ? 

Write  :         One-third  of  twelve  is  four. 
Eight  and  four  are  twelve. 
Twelve  minus  eight  are  four. 
Four  and  eight  are  twelve. 
Twelve  minus  four  are  eight. 
Twelve  divided  by  four  are  three. 
Three  fours  are  twelve. 
One-fourth  of  twelve  is  three. 

Fill  out  these  expressions : 


8+    4  = 

8 

4 

12. 

12-4  = 

12 

4 

8. 

4+    8  = 

4 

8 

12. 

12-8  = 

12 

8 

4. 

9+    3  = 

9 

3 

12. 

12-3  = 

12 

3 

9. 

3+    9  = 

3 

9 

12. 

12-9  = 

12 

9 

3. 

10+2  = 

10 

2 

12. 

12  -  10  = 

12 

10 

2. 

2  +  10  = 

2 

10 

12. 

12-2  = 

12 

10 

2. 

6  twos  = 

4  + 

=  12. 

4  threes  = 

8  + 

=  12. 

3  fours    = 

9  + 

=  12. 

i  of  12  is 

10  + 

=  12. 

i  of  12  is 

3  + 

=  12. 

12  divided  by  2  = 

2  + 

=  12. 

12  divided  by  3  = 

12- 

=    8. 

12  divided  by  4  = 

12- 

=    4. 

THE   NUMBER   TWELVE.  251 

If  Ned  has  eight  cents,  and  Harry  four  cents,  how  many 
cents  have  both  ?  If  Ned  pays  Harry  a  cent,  how  many 
cents  will  both  have  ?  How  many  cents  will  each  have  ? 
Seven  cents  and  five  cents  are  how  many  cents  ? 

Give  examples  for  seven  and  five. 

If  I  have  seven  peaches,  how  many  more  peaches  must  I 
have  to  make  a  dozen  peaches  ? 

If  I  lack  five  of  a  dozen,  how  many  have  I  ? 

Seven  candle-sticks  were  on  the  table  a  moment  ago. 
Now  there  are  twelve.  How  many  have  been  added  to  the 
number  that  was  there  first? 

A  dozen  turkeys  went  off  in  the  wet  grass  one  morning, 
and  only  seven  came  back.     How  many  were  missing  ? 

Twelve  milk-cans  were  drying  on  a  bench,  but  the  wind 
blew  seven  off  on  the  ground.  How  many  cans  were  left 
on  the  bench  ? 

John  had  but  five  cents  this  morning.  Now  he  has 
twelve  cents.  How  many  cents  has  he  earned  through  the 
day? 

Express  on  the  board  the  difference  between  twelve  and 
seven. 

Express  on  the  board  the  sum  of  seven  and  five. 

Express  the  difference  between  twelve  and  five. 


Ben  had  seven  nuts,  George  had  five  nuts.  How  many 
nuts  had  they  together  ?  Ben  gave  one  of  his  nuts  to 
George.  How  many  had  both  then  ?  How  many  had  each  ? 
Six  nuts  and  six  nuts  are  how  many  nuts? 

Give  me  stories  for  six  and  six. 

Twelve  is  how  many  more  than  six  ? 

Six  and  how  many  more  are  twelve  ? 

If  there  are  a  dozen  books  in  one  pile,  and  six  in  another 
pile,  how  many  more  books  are  in  one  pile  than  in  the 
other  ? 


252  FIRST  STEPS   IN  NUMBER. 

If  I  have  a  dozen  beautiful  colored  leaves,  and  you  have 
only  six  leaves,  how  many  more  have  I  than  you  ? 

I  have  six  beautiful  butterflies  that  were  given  me  by  a 
little  boy.  He  says  he  is  going  to  give  me  a  dozen.  How 
many  more  will  he  need  to  give  me  ? 

Express  on  the  board  the  sum  of  six  and  six. 

Express  the  difference  of  twelve  and  six. 

If  six  and  six  are  twelve,  how  many  sixes  are  there  in 
twelve  ? 

Divide  twelve  by  six,  and  see  if  two  is  the  answer. 

Twelve  apples  will  make  how  many  puddings  if  six 
apples  are  required  for  each  pudding  ? 

Twelve  yards  of  dress  goods  will  make  how  many  dresses 
if  six  yards  are  required  for  each  dress  ? 

"Who  has  a  story  for  twelve  divided  by  six  ? 

If  there  are  two  sixes  in  twelve,  how  many  sixes  make 
twelve? 

Two  window  sashes,  with  six  panes  of  glass  in  each  sash, 
contain  how  many  panes  of  glass  ? 

Two  cubes  have  how  many  faces  ? 

How  much  will  two  six-cent  books  cost  ? 

How  much  will  two  lamps  cost  at  six  dollars  apiece  ? 

I  sent  two  books  through  the  mail.  One  weighed  six 
ounces,  and  the  other  weighed  twice  as  much.  How  many 
ounces  did  the  heavier  book  weigh  ? 

What  two  equal  numbers  make  twelve  ? 

What  then  is  one-half  of  twelve  ? 

What  distance  is  one-half  of  twelve  miles  ? 

How  many  eggs  in  a  half-dozen  eggs  ? 

How  many  months  in  half  a  year  ? 

This  rule  is  twelve  inches  long.  How  long  is  half  the 
rule? 

If  twelve  persons  can  sit  on  two  settees,  how  many  per- 
sons can  sit  on  one  settee  ? 


THE   NUMBER  TWELVE.  253 

It  takes  twelve  hours  for  the  short  hand  to  go  round  the 
face  of  the  clock.  How  many  hours  will  it  take  the  hand 
to  go  half-way  round  ? 

If  a  gentleman  gets  twelve  letters  in  a  single  mail,  and 
answers  half  of  them  immediately,  how  many  does  he  an- 
swer at  once  ? 

Tell  me  a  story  for  one-half  of  twelve? 

Express  on  the  board  : 

The  sum  of  six  and  six. 

The  difference  of  twelve  and  six. 

One-half  of  twelve. 

Twelve  divided  by  six. 

The  number  of  sixes  that  make  twelve. 

Fill  out  these  expressions : 


i  of  12 

= 

6  + 

=  12. 

iof  12 

= 

7  + 

=  12. 

i  of  12 

= 

8  + 

=  12. 

6  twos 

= 

9  + 

=  12. 

4  threes 

= 

10  + 

=  12. 

3  fours 

= 

12- 

=    6. 

2  sixes 

= 

12- 

=    0. 

12-2 

= 

12- 

=    7. 

12-3 

=: 

12- 

=    1. 

12-4 

= 

12- 

=    8. 

12-5 

= 

12- 

=    2. 

12-6 

= 

12- 

=    9. 

12-12 

= 

12-^ 

=    3. 

12  -  11 

= 

12- 

=  10. 

12-10 

= 

12- 

=    4. 

12-9 

= 

12- 

=    5. 

12-8 

= 

12- 

=  11. 

254 


FIRST   STEPS    IN   NUMBER. 


The 

Sign  X. 

Read  these  expressions : 

2  twos     =  4. 

2  sixes    =  12. 

2  threes  =  6. 

3  fours    =  12. 

3  threes  =  9. 

2  fives     =  10. 

3  twos     =  6. 

5  twos    =  10. 

2  fours    =  8. 

4  threes  =  12. 

4  twos     =  8. 

6  twos    =  12. 

(At  each  correct  reading 

introduce  the  sign  of  multipli- 

cation  together  with  the  required  figure.     The  expressions 

will  then  stand : 

2x2  =  4. 

2  X  6  =  12. 

2x3  =  6. 

3  X  4  =  12. 

3X3  =  9. 

2  X  5  =  10. 

3x2  =  6. 

5  X  2  =  10. 

2x4  =  8. 

4  X  3  =  12. 

4x2  =  8. 

6x2  =  12.) 

Read  these  expressions : 

Write  in  this  new  way : 

Two  twos  are  four. 

Eight  zeros  are  zero. 

Two  sixes  are  twelve. 

Eleven  ones  are  eleven. 

Five  ones  are  five. 

Twelve  ones  are  twelve. 

Seven  ones  are  seven. 

Six  twos  are  twelve. 

Complete  :    2  X  2  = 

2         6  =  12. 

3x2  = 

2         5  =  10.       . 

4x2  = 

3         4  =  12. 

5x2  = 

4         3  =  12. 

6X2  = 

6         2  =  12. 

2x3  = 

2        4=    8. 

3x3  = 

4        2==    8. 

4x3  = 

2        3=6. 

2x4  = 

3         2=6. 

3x4  = 

3         3=    9. 

2x5- 

5         2  =  10. 

2x6  = 

2        2=    4. 

THE  NUMBER  TWELVE.  255 


The  Foot. 


You  may  eacli  take  one  of  these  strips  of  paper.  Who 
knows  how  long  the  strip  of  paper  is  ?     It  is  a  foot  long. 

Draw  a  line  on  the  board  a  foot  long ;  draw  another  line 
just  as  long  extending  in  some  other  direction.  How  long 
is  it? 

Measure  off  a  foot  on  the  edge  of  the  table ;  on  the  edge 
of  the  platform  ;  on  the  edge  of  the  blind ;  on  the  edge  of 
the  blackboard ;  on  the  round  of  the  chair ;  on  the  round 
of  the  settee ;  on  the  leg  of  the  chair ;  on  the  leg  of  the 
settee ;  on  the  desk ;  on  the  piano ;  on  your  slate  if  you 
can.  Whose  slate  has  a  side  a  foot  long?  Extend  your 
arms  with  your  hands  a  foot  apart.  I  will  measure  the 
distance  between  your  hands. 

Lay  oiF  on  your  arm  the  distance  of  a  foot.  I  will  s^e  if 
my  foot-measure  will  just  fit  the  distance. 

What  have  you  seen  at  home  that  is  a  foot  in  length  ? 
Who  has  seen  any  one  measure  with  a  foot-rule  before  to- 
day ? 

This  foot-rule  is  marked  off  into  short  distances.  How 
long  is  each  distance?  (An  inch.)  How  many  inches  long 
is  this  foot-rule  ?  How  many  inches  long  is  the  line  you 
drew  ?  How  many  inches  apart  are  your  hands  if  you  hold 
them  a  foot  apart  ?  How  many  inches  is  your  step  if  it  is 
a  foot  long  ?  If  you  stand  a  foot  apart  from  each  other, 
how  many  inches  apart  are  you  ? 

Tell  me  a  story  for  twelve  inches  in  a  foot. 

How  many  inches  in  half  a  foot  ? 

If  you  draw  a  square  a  half  a  foot  on  each  side,  how 
many  inches  long  is  a  side  of  the  square  ? 

In  one-fourth  of  a  foot  how  many  inches?  Which  is 
longer,  one-half  of  a  foot  or  one-fourth  of  a  foot  ?  How 
many  quarters  of  a  foot  does  it  take  to  make  a  half  a  foot  ? 


256  FIRST  STEPS   IN   NUMBER. 

How  many  inches  in  one-third  of  a  foot?  Whicli  is 
more,  one-half,  one-third,  or  one-fourth  of  a  foot?  Which 
is  more,  one-third  or  one-fourth  of  a  foot  ? 

Write  on  the  board  what  you  have  found  out  about  the 
number  of  inches  in  a  foot,  as  I  have  written  it  (12  inches 
=  1  foot).     Write  the  expression  a  half  dozen  times. 


Exercise  for  Review. 

Six  books  have  how  many  covers  ? 

Six  sheets  of  note-paper  have  how  many  leaves  ? 

Six  pairs  of  scissors  have  how  many  blades  ? 

Let  this  circle  represent  a  wheel.  Let  these  eight  lines 
represent  spokes.  How  many  more  spokes  does  it  need  to 
have*  twelve  spokes  ? 

There  are  twelve  panes  of  glass  in  each  of  my  windows. 
The  panes  are  arranged  in  rows  of  three  each.  How  many 
rows  in  each  window  ? 

I  can  make  a  pretty  design  by  drawing  four  maple 
leaves.  If  I  make  three  such  designs,  how  many  maple 
leaves  shall  I  draw  ? 

Nellie  is  putting  a  border  on  the  board  in  squares.  She 
puts  two  leaves  in  each  square.  How  many  leaves  will 
she  put  in  five  squares  ?  in  six  squares  ? 

Annie  is  drawing  a  border  in  circles.  She  will  put  six 
leaves  in  each  circle.  How  many  leaves  will  she  put  in 
two  circles  ? 

Cyrus  has  just  finished  the  twelfth  leaf  of  his  writing- 
book,  and  is  half  way  through  the  book.  How  many  more 
leaves  has  he  to  write  ?  If  he  writes  three  leaves  a  week, 
how  many  weeks  will  be  required  to  finish  the  book  ?  What 
part  of  a  month?  What  part  of  the  term  if  there  are 
twelve  weeks  in  a  term  ? 


THE  NUMBER  TWELVE.  257 

I  have  a  silver  vase  with  three  cups.  How  many  cups 
have  four  such  vases  ? 

How  many  handles  have  six  trunks  if  three  of  them  have 
lost  a  handle  each  ? 

Three  squares  have  how  many  sides  ? 

Four  triangles  have  how  many  sides  ? 

Six  cylinders  have  how  many  plane  faces  ? 

Two  cubes  have  how  many  faces  ? 

A  foot-rule  is  how  many  inches  in  length?  One-half 
a  foot  is  how  many  inches  ?  One-fourth  of  a  foot  ?  One- 
third  of  a  foot  ? 

Six  clothes-pins  have  how  many  legs  ? 

How  many  heads  have  eleven  clothes-pins  ? 

How  many  eyes  have  eleven  buttons  ? 

A  half  dozen  boys  were  watching  a  monkey  dance,  and 
five  more  came  to  see  the  fun.  How  many  boys  were 
watching  the  monkey  then  ? 

The  Wide  Awake  comes  once  a  month.  I  have  the 
numbers  for  half  a  year,  and  for  five  more  months.  How 
many  numbers  have  I  ? 

If  two  books  come  each  month,  how  many  shall  I  get  in 
five  months  and  a  half? 

If  two  come  each  month,  how  often  do  they  come  by  the 
week'?    How  many  shall  I  have  received  in  twelve  weeks  ? 

I  have  read  of  a  giant  that  was  seven  feet  tall.  A  room 
in  your  house  is  ten  feet  high.  How  much  difierence  is 
there  between  the  height  of  your  room  and  this  giant  ? 

A  lady  brought  home  six  monkeys  and  five  parrots  as 
pets.  She  tied  the  monkeys  to  the  fence,  and  hung  the 
parrot  cages  on  a  tree  near  the  fence.  How  many  pets 
could  the  children  count  as  they  stopped  to  watch  them  ? 

There  were  seven  visiting  cards  in  my  card-receiver  this 
morning.  Now  there  are  eleven.  How  many  callers  have 
I  had  during  the  day  if  each  brought  a  card  ? 


258  FIRST  STEPS   IN   NUMBER. 

There  are  eight  tones  in  the  musical  scale.  If  you  can- 
sing  the  scale  and  three  more  tones,  how  many  tones  cap 
you  sing? 

If  there  are  three  ripe  pumpkins,  and  eight  green  pump- 
kins in  the  field,  how  many  pumpkins  are  in  the  field  ? 

If  you  are  to  go  away  from  home  the  eleventh  of  the 
month,  and  it  is  now  the  eighth  of  the  month,  how  many 
days  have  you  at  home  counting  to-day  ? 

From  the  third  of  the  month  to  the  eleventh  of  the 
month  are  how  many  days  counting  the  third  ? 

Neddie  and  Harry  were  counting  the  rails  in  a  fence. 
Neddie  counted  by  ones,  and  Harry  counted  by  twos.  Who 
counted  them  quickest?  How  could  you  count  them 
quicker  still  ? 

If  you  count  twelve  by  ones,  how  many  numbers  must 
you  name  over  to  yourself?  If  you  count  twelve  by  twos, 
how  many  numbers  will  you  name  over  to  yourself?  If 
you  count  twelve  by  threes,  how  many  numbers  will  you 
name? 

You  may  go  about  the  room  and  make  believe  you  are 
out  of  doors.  When  you  come  back  I  shall  ask  you  what 
you  saw,  how  many  you  saw,  and  how  you  counted  them. 
What  did  you  see,  Ellen  ?  (Trees  in  an  orchard.)  How 
many?  (Twelve.)  How  did  you  count  them?  (By 
threes.)  Let  me  hear  you  count  twelve  by  threes.  What 
did  you  see,  Grace?  (Doves  in  the  path.)  How  many? 
(Ten.)  How  did  you  count  them  ?  (By  twos.)  Count 
ten  by  twos.  What  did  you  see,  Henry?  (Cows  in  the 
pasture.)  How  many?  (Nine.)  How  did  you  count 
them?  (By  threes.)  Count  nine  by  threes.  What  did 
you  see,  Willie?  (Butterflies.)  How  many?  (Seven.) 
How  did  you  count  them  ?  (By  ones.)  Why  did  you 
count  them  by  ones?  (Because  they  were  all  flying 
about.) 


THE   NUMBER   TWELVE.  259 

You  may  form  a  circle.  George  may  stand  in  the  centre 
and  remain  until  he  fails  to  tell  me  how  many  : 

Four  and  three?  Six  and  three? 

Eight  and  three?  Seven  and  three? 

Nine  and  three  ?  Five  and  three  ? 

Five  and  four  ?  Seven  and  four  ? 

Six  and  four  ?  Eight  and  four  ? 

Seven  and  five  ?  Six  and  five  ? 

Six  and  six  ?  Two  sixes  ? 

Two  fives?  Two  threes? 

Two  fours  ?  Three  threes  ? 

Three  twos  ?  Three  fours  ? 

Each  take  twelve  blocks.  Call  them  chickens.  Close 
your  eyes.  (Teacher  removes  a  number  from  each  group.) 
Open  your  eyes  and  tell  me  about  your  loss. 

Mary.  I  had  twelve  chickens ;  now  I  hjave  but  eight.  I 
have  lost  four. 

Willie.  I  had  twelve  chickens ;  now  I  have  but  six.  I 
have  lost  six. 

Nettie,  I  had  twelve  chickens  and  have  lost  five,  so  I  have 
but  seven  chickens. 

How  many  have  you  lost,  Harry?  (Three.)  Mamie? 
(Two.)     Bertie?     (Eight.)     Susie?     (Nine.) 

Each  take  five  blocks.  Call  them  cents.  Close  your 
eyes  again.  (Teacher  adds  a  number  to  each  group.)  Open 
your  eyes  and  tell  me  what  you  have  gained. 

Annie.  I  had  five  cents ;  now  I  have  eight  cents.  I  have 
gained  three  cents. 

Helen.  I  had  five  cents ;  now  I  have  ten  cents.  I  have 
gained  five  cents. 

How  many  have  you  gained,  John?  (Six.)  Lizzie? 
(Four.)  James?  (Two.)  Ned?  (Five.)  Ralph?  (Seven.) 
Henry?    (Three.)    George?    (Eight.) 


CHAPTER  XIII. 

THE  NUMBER   THIRTEEN. 


§  35.    The  Number  Thirteen. 

Take  ten  splints.  Put  them  into  a  bundle,  and  put  this 
band  about  them. 

Take  three  more  splints.  How  many  are  in  the  bundle  ? 
How  many  more  have  you  ?  Who  knows  how  many  each 
has  all  together  ?  Thirteen  is  the  right  number.  Put  the 
splints  back.  Take  thirteen  the  quickest  way.  (One  ten 
and  three.)  What  did  you  take  ?  (One  ten  and  three.) 
One  ten  and  three,  are  how  many  ?  Write  this  in  words  on 
the  board.     (One  ten  and  three  are  thirteen.) 

Show  me  the  number  of  tens  in  thirteen.  (Let  teacher 
put  the  figure  1  over  the  phrase  "  one  ten.")  Show  me  how 
many  ones  besides.  (Let  the  figure  3  be  placed  over  the 
word  three.)  Who  can  express  thirteen  in  figures  ?  Show 
me  the  figure  that  stands  for  the  number  of  tens ;  for  the 
number  of  ones  besides.  Express  twelve  below  thirteen. 
Express  eleven  in  the  same  column.  Express  ten.  How 
many  tens  in  each  of  these  numbers  ?  •  How  many  tens 
all  together  ?     How  many  ones  all  together  ? 

Ralph  brought  me  ten  cents  for  a  book,  and  three  cents 
for  a  pencil.     How  many  cents  did  he  bring  me  ? 

Ten  crackers  and  three  crackers  are  said  to  be  a  baker's 
dozen.     How  many  make  a  baker's  dozen? 

If  there  are  ten  Japanese  lanterns  on  a  tree,  and  I  hang 
three  more  on  the  tree,  how  many  Japanese  lanterns  are 
then  on  the  tree  ? 


THE  NUMBER  THIRTEEN.  261 

If  there  are  thirteen  Japanese  lanterns  in  a  tree,  and 
three  burn  out,  how  many  will  remain  in  the  tree  ? 

If  there  are  thirteen  persons  in  our  family,  and  three  go 
away,  how  many  persons  will  remain  in  our  family  ? 

If  there  are  thirteen  sticks  of  wood  in  the  basket,  and  I 
put  three  in  the  fire,  how  many  will  remain  in  the  basket  ? 

If  three  must  be  added  to  ten  to  give  thirteen,  what 
number  must  be  taken  from  thirteen  to  leave  ten  ?  Since 
thirteen  minus  three  equals  ten,  thirteen  minus  ten  will 
equal  what  number  ? 

What  is  the  difference  between  thirteen  and  ten  ?  between 
thirteen  and  three  ? 

If  one  kind  of  syrup  is  ten  cents  a  quart,  and  another 
kind  is  thirteen  cents  a  quart,  what  is  the  difference  in 
price  ? 

Mabel  is  three  years  old,  and  John  is  thirteen  years  old. 
What  is  the  difference  in  their  ages  ? 

Express  on  the  board  the  sum  of  ten  and  three. 
(10  +  3  =  13.) 

Express  the  difference  of  thirteen  and  three. 
(13  -  3  -  10.) 

Express  the  difference  of  thirteen  and  ten. 
(13  -  10  -  3.) 

I  wish  for  a  story  for  what  you  have  expressed  on  the 
board . 

If  there  were  ten  boys  standing  in  one  group,  and  three 
boys  in  another  group,  how  many  boys  were  there  in  both 
groups  ?  If  one  of  the  ten  boys  should  join  the  other  group, 
how  many  would  there  be  in  both  groups  ?  How  many  in 
each  group  ?   Nine  boys  and  four  boys  are  how  many  boys  ? 

Nine  hours  of  work  and  four  hours  of  work  are  how 
many  hours  of  work  ? 


262  FIRST   STEPS   IN   NUMBER. 

Who  has  a  story  for  nine  and  four  ? 

What  number  must  be  put  with  nine  to  give  thirteen  ? 
Then  four  subtracted  from  thirteen  will  give  what  number  ? 

There  were  thirteen  swallows'  nests  in  a  sand-bank,  but 
the  bank  gave  way  and  destroyed  four  nests.  How  many 
were  left  ? 

I  had  a  ten-cent  piece  and  a  three-cent  piece  of  money. 
I  spent  four  cents.     How  many  cents  did  I  have  then  ? 

If  you  have  two  five-cent  pieces  of  money,  and  a  three- 
cent  piece,  and  spend  the  three-cent  piece  and  one  more 
cent,  how  many  cents  will  you  have  ? 

Nine  and  what  number  are  thirteen  ? 

What  number  subtracted  from  thirteen  leaves  nine  ? 

Since  thirteen  minus  four  leaves  nine,  thirteen  minus 
nine  will  leave  what  number  ? 

Tell  a  story  for  thirteen  minus  nine. 

Express  on  the  board  the  sum  of  nine  and  four. 

Express  the  diiFerence  of  thirteen  and  four. 

Express  the  difierence  of  thirteen  and  nine. 

Tell  me  what  to  put  in  these  blanks : 


10+3  = 

10 

3 

13. 

9+    4  = 

9 

4 

13. 

13-3  = 

13 

3 

10. 

13-4  = 

13 

4 

9. 

13  -  10  = 

13 

10 

3. 

13-9  = 

13 

9 

4. 

A  squirrel  has  four  toes  on  each  forefoot,  and  fiye  toes 
on  each  hind  foot.  How  many  toes  has  he  on  both  fore- 
feet and  one  hindfoot  ? 

Two  tables  with  each  four  legs,  and  one  table  with  five 
legs,  have  how  many  legs  all  together? 


THE   NUMBER   THIRTEEN.  263 

Four  two-cent  stamps  and  a  five-cent  stamp  cost  how 
much? 

A  bench  that  is  eight  feet  long  and  five  feet  wide  meas- 
ures how  many  feet  on  one  side  and  one  end  together? 

Eight  and  five  equal  what  number? 

Eight  and  what  number  equal  thirteen  ? 

Eight  is  how  many  less  than  thirteen  ? 

If  there  are  thirteen  matches  in  a  card,  and  I  use  five, 
how  many  will  be  left  ? 

If  to-day  is  the  thirteenth  of  the  month,  how  many  days 
ago  was  the  eighth  of  the  month  ? 

If  this  room  is  thirteen  feet  in  width,  how  much  wider  is 
it  than  a  small  room  that  is  only  eight  feet  wide  ? 

A  room  is  thirteen  feet  wide,  and  eight  feet  high.  What 
is  the  difference  in  width  and  height  ? 

Give  me  a  story  for  what  I  express : 

8  -f  5  =  13.  13  -  8  --    5. 

5  +  8-13.  13  X  1  =  13. 

13  -  5  =    8.  12+1-13. 

13-1-12.  11  +  2  -  13. 


Henry  had  eight  cents,  and  John  had  five  cents.  How 
many  cents  had  both  ?  Henry  paid  John  one  cent.  How 
many  cents  had  each  of  the  boys  then  ?  How  many  cents 
had  they  together  ?  What  new  pair  of  numbers  have  you 
just  found  make  thirteen  ? 

Tell  me  a  story  for  seven  and  six. 

A  square  and  a  triangle  and  a  six-sided  figure  have  how 
many  sides? 

How  many  weeks  and  days  in  thirteen  days  ? 

George  had  thirteen  cents.  If  he  had  two  three-cent 
pieces,  and  the  rest  of  his  money  in  one-cent  pieces,  how 
many  one-cent  pieces  of  money  had  he  ? 


264  FIRST   STEPS   IN   NUMBER. 

There  are  thirteen  children  in  one  division,  and  six  of 
the  children  are  girls.    How  many  boys  are  in  the  division  ? 

Of  thirteen  sheep  in  a  flock,  six  were  sold.  How  many 
were  left  of  the  flock  ? 

There  are  thirteen  pegs  on  a  hat-rack.  Six  are  covered 
with  hats.     How  many  can  be  seen  ? 

Complete  these  expressions : 


6+    7  = 

6  + 

=  13. 

13-6  = 

13- 

=    6. 

13-7  = 

13- 

=    7. 

7+    6  = 

7  + 

=  13. 

8+    5  = 

8  + 

=  13. 

18-5  = 

13- 

=    8. 

13-8  = 

13- 

=    5. 

5+    8  = 

5  + 

=  13. 

9+    4  = 

9  + 

=  13. 

13-4  = 

13- 

=    9. 

13-9  = 

13- 

=    4. 

4+    9  = 

4  + 

=  13. 

10+3  = 

10  + 

=  13. 

13  -  10  = 

13- 

=    3. 

13-3  = 

13- 

=  10. 

OHAPTEE    XIV. 

THE    NUMBER    FOURTEEN. 


§  36.   The  Number  Fourteen. 

Take  a  bundle  of  ten  splints.  Take  four  more  splints. 
How  many  splints  have  you  taken  in  all  ?  Show  me  what 
makes  fourteen.  Tell  me  what  makes  fourteen.  Write  it 
in  words  on  the  board.     (One  ten  and  four  are  fourteen.) 

Who  will  express  fourteen  in  figures  ? 

Which  figure  shows  the  number  of  tens  in  fourteen  ? 
Which  figure  shows  the  number  of  ones  that  must  be  put 
with  ten  to  give  fourteen? 

Express  thirteen  just  below  fourteen.  Express  twelve  in 
the  same  column ;  eleven ;  ten.  How  many  tens  in  four- 
teen? in  thirteen?  in  twelve?  in  eleven?  in  ten?  Point 
to  the  column  of  tens. 

What  must  be  put  with  ten  to  give  fourteen?  to  give 
thirteen  ?  to  give  twelve  ?  to  give  eleven  ?  to  give  ten  ? 
Point  to  the  column  of  ones. 

A .  ten-cent  piece  of  money,  and  two  two-cent  pieces  of 
money,  are  how  much  money  ? 

If  there  are  ten  buttons  on  a  string,  and  I  put  four  more 
buttons  on  the  string,  how  many  buttons  will  then  be  on 
the  string? 

I  wish  to  place  my  boys  in  rows  with  fourteen  in  each 
row.  After  placing  them  I  find  I  have  only  four  boys  for 
the  last  row.  How  many  more  do  I  need  to  have  the  row 
filled? 


266  FIRST  STEPS   IN   NUMBER. 

A  room  is  fourteen  feet  wide.  How  many  feet  will  a 
ten-foot  pole  lack  of  reaching  across  the  room  ? 

There  were  fourteen  rails  along  the  balustrade,  but  four 
got  broken.  How  many  rails  were  then  along  the  balus- 
trade ? 

Some  boys  who  went  for  berries  took  with  them  a  four- 
teen-quart  pail.  They  picked  ten  quarts  of  berries.  How 
many  more  quarts  would  their  pail  hold  ? 

I  have  ten  pictures  in  my  album,  and  it  will  hold  four 
more  pictures.     How  many  pictures  will  my  album  hold  ? 

Take  fourteen.  How  many  tens  have  you  ?  How  many 
ones  besides  ?  How  many  twos  in  ten  ?  How  many  twos 
in  four?  How  many  twos  in  ten  and  in  four  together? 
How  many  twos  in  fourteen  ? 

If  I  sell  fourteen  pencils  in  one  morning,  and  sell  two  to 
each  child,  to  how^  many  children  shall  I  sell  the  pencils  ? 

If  you  have  fourteen  cents  in  two-cent  pieces,  how  many 
two-cent  pieces  have  you  ? 

If  a  gem-pan  has  fourteen  cups,  two  in  each  row,  how 
many  rows  of  cups  has  it  ? 

If  the  blackboard  is  fourteen  feet  long,  how  many  two- 
foot  rules  could  be  placed  along  its  edge  ? 

If  a  room  is  fourteen  feet  long,  how  many  chairs,  each 
two  feet  in  width,  can  be  placed  along  the  side  of  the  room  ? 

If  fourteen  pounds  of  butter  are  put  into  lumps  which 
weigh  two  pounds  each,  how  many  lumps  of  butter  can  be 
made  from  the  fourteen  pounds  ? 

Who  has  examples  for  fourteen  divided  by  two? 

Express  this  fact  a  half  dozen  times  on  the  board. 
(14  divided  by  2  =  7.) 

If  each  chestnut-burr  has  two  nuts  in  it,  how  many  burrs 
must  you  find  to  get  fourteen  nuts  ?  Seven  chestnut-burrs 
then,  with  two  nuts  in  each  burr,  will  have  how  many 
chestnuts  ? 


THE   NUMBER   FOURTEEN.  267 

Seven  boys  will  wear  how  many  shoes  ? 

Seven  pairs  of  skates  are  how  many  skates  ? 

Seven  yoke  of  oxen  are  how  many  oxen  ? 

Seven  spans  of  horses  are  how  many  horses  ? 

I  have  two  cents.  How  many  cents  must  you  have  to 
have  seven  times  as  many  cents  as  I  have  ? 

Ada  is  two  years  old.  Jennie's  age  is  seven  times  Ada's 
age.     How  old  is  Jennie  ? 

If  we  eat  two  pounds  of  butter  a  day  on  the  table,  how 
many  pounds  shall  we  eat  in  a  week  ? 

If  I  write  two  letters  a  day,  how  many  letters  shall  I 
write  in  a  week  ? 


Fill  out: 

10+4  = 

10 

4        14. 

14-4  = 

14 

4        10. 

14  -  10  = 

14 

10          4. 

4+10  = 

4 

10        14. 

7x    2  = 

7 

2        14. 

6x    2  = 

14  divided  by  2  = 

5x    2  = 

12  divided  by  2  = 

4x2  = 

10  divided  by  2  = 

3x    2  = 

8  divided  by  2  = 

2X    2  = 

6  divided  by  2  = 

The  Sign  ^. 

Who  knows  what  words  are  omitted  in  these  expressions : 


6 

2  =  3. 

12 

2  =  6. 

8 

4  =  2. 

12 

8  =  4. 

9 

3  =  3. 

12 

4  =  3. 

8 

2  =  4. 

12 

6  =  2. 

14 

2=7. 

12 

12  =  1. 

(Let  the  teacher  introduce  the  sign  of  division  as  the 
correct  phrase  is  given  in  each  case.  Have  the  expressions 
in  their  new  form  read.) 


14- 

-    2  =  7 

14- 

-14  =  1 

14- 

-    2=7 

12- 

-    G  =  2 

12- 

-    2  =  6 

12- 

-4  =  3. 

^68  FIRST  STEPS   IN   NUMBER. 

Read  these  expressions : 

2-^1::-      2. 

7-v-l-    7. 
14  -  1  -  14. 

12  --  1  =  12. 

13  -^  1  -  13. 
12 --3-    4. 

Write  in  the  new  way  : 

Eight  divided  by  two  are  four. 
Ten  divided  by  two  are  five. 
Twelve  divided  by  two  are  six. 
Fourteen  divided  by  two  are  seven. 
Eight  divided  by  four  are  two. 
Ten  divided  by  five  are  two. 
Twelve  divided  by  six  are  two. 
Nine  divided  by  three  are  three. 
Twelve  divided  by  three  are  four. 
Twelve  divided  by  four  are  three. 


Take  fourteen.  If  you  take  one  from  the  bundle  of  tens 
and  put  it  with  four,  what  two  numbers  will  you  show  me  ? 

Nine  and  five  are  how  many  ? 

Tell  me  a  story  for  nine  and  five. 

It  is  nine  hours  since  I  got  up  this  morning.  If  I  sit  up 
five  hours  longer,  how  many  hours  will  there  be  in  my  day  ? 

A  room  in  our  cottage  is  nine  feet  high.  The  church  is 
five  feet  higher.     How  high  is  the  church  ? 

If  I  have  three  three-cent  pieces,  and  a  five-cent  piece  of 
money,  how  much  money  have  I  ? 

Annie  bought  three  peaches  at  three  cents  apiece,  and 
five  one-cent  rolls  of  lozenges.  How  much  money  did  she 
spend  ? 

I  had  fourteen  dollars  in  dollar  bills.  I  exchanged  five 
of  the  bills  for  a  five-dollar  bill.  How  many  dollar-bills 
had  I  then? 


THE   NUMBER  FOURTEEN. 


269 


There  are  fourteen  days  in  two  weeks.  If  five  days  are 
stormy,  how  many  days  are  pleasant  ? 

I  received  fourteen  letters  this  morning,  and  have  an- 
swered five.     How  many  more  have  I  to  answer  ? 

Jennie  had  fourteen  cocoanut  cakes.  She  gave  three  to 
each  of  her  two  brothers,  kept  three  herself,  and  gave  the 
rest  to  her  mother.     How  many  did  she  give  her  mother  ? 

I  sent  two  packages  by  mail  that  cost  fourteen  cents.  If 
one  of  the  packages  required  three  three-cent  stamps,  how 
much  did  it  cost  to  send  the  other  package  ? 

If  white  sugar  is  nine  cents  a  pound,  and  maple  sugar  is 
fourteen  cents  a  pound,  what  is  the  difference  in  price  ? 

I  bought  two  chairs  last  week.  One  cost  five  dollars 
and  the  other  fourteen  dollars.  What  was  the  difference 
in  price  ? 

Express  on  the  board  the  sum  of  nine  and  five. 

Express  the  difference  of  fourteen  and  nine. 

Express  the  difference  of  fourteen  and  five. 

Fill  out  these  expressions : 


9  + 
14- 
14- 

5  + 
10  + 
14- 


5  = 
9  = 
5  = 
9  = 

4  = 
4  = 


14  -  10  = 
4  +  10  = 

7x    2  = 


14-f- 
12- 
10 

8 

6 

4 

2^ 


2  = 
2  = 
2  = 
2  = 
2  = 
2  = 
2  = 


9 

5 

14. 

14 

9 

5. 

14 

5 

9. 

5 

9 

14. 

10 

4 

14. 

14 

.  4 

10. 

14 

10 

4. 

4 

10 

14. 

7 

2 

14. 

14 

2 

7. 

12- 

-3  = 

9-f 

-3  = 

6- 

-3  = 

3^ 

-3  = 

12^ 

-4  = 

8^ 

-4=^ 

270  FIRST  STEPS   IN   NUMBER. 

Divide  fourteen  into  two  such,  numbers,  tliat  one  number 
will  be  two  more  than  the  other  number. 

What  are  the  two  numbers  ? 

Tell  me  stories  for  eight  and  six. 

Two  squares  and  two  triangles  have  how  many  corners 
together  ? 

A  spider  with  eight  legs,  and  a  fly  with  six  legs,  have 
how  many  legs  all  together  ? 

Four  two-cent  pieces  of  money,  and  two  three-cent  pieces 
of  money,  are  how  much  money  ? 

I  saw"  two  dogs  and  three  boys  scampering  down  the 
lane.     How  many  feet  were  scampering  over  the  path  ? 

Two  horses  got  in  the  farmer's  clover,  and  three  boys 
went  to  drive  them  out.  How  many  feet  were  there  tram- 
pling down  the  clover? 

A  farmer,  who  had  fourteen  sheep,  sold  six  sheep.  How 
many  sheep  had  he  left  ? 

I  ordered  some  dress  goods  two  weeks  ago,  and  had  to 
wait  six  days  before  it  came.  How  many  days  ago  did 
I  receive  the  goods  ? 

A  man  who  had  ten  cows  and  four  horses  sold  six  ani- 
mals.    How  many  had  he  left? 

If  you  have  three  three-cent  pieces  of  money,  and  a  five- 
cent  piece,  and  spend  two  three-cent  pieces,  how  much 
money  will  you  have  left  ? 

If  a  hall  is  fourteen  feet  high,  and  a  man  six  feet  in 
height,  what  is  the  difference  in  height  ? 

A  boy,  who  had  fourteen  quarts  of  berries  to  sell,  has 
sold  a  half-dozen  quarts.  How  many  quarts  has  he  left  to 
sell? 

Frank  picked  his  pint-cup  full  of  raspberries  fourteen 
times.  Three  quarts  of  the  raspberries  were  eaten  on  the 
table,  and  the  rest  made  into  sauce.  How  many  pints  of 
the  raspberries  were  made  into  sauce  ? 


THE   NUMBER  FOURTEEN. 


271 


What  number  taken  from  fourteen  leaves  six?  What 
number  taken  from  fourteen  leaves  eight  ? 

Eight  and  how  many  are  fourteen  ? 

Six  and  how  many  are  fourteen  ? 

Fourteen  are  how  many  more  than  six  ? 

Fourteen  are  how  many  more  than  eight  ? 

Express  the  sum  of  eight  and  six,  on  the  board,  a  half 
dozen  times. 

Express  the  difference  of  fourteen  and  six,  half  as  many 
times. 

Fill  out  the  blanks  I  have  left : 


8+    6  = 

14  - 

-    4  = 

6^    3  = 

9+    5  = 

7x    2  = 

9-v-    3  = 

10+4  = 

14- 

-    2  = 

|of    2  = 

14-8  = 

12- 

-    4  = 

iof   4  = 

14-6  = 

8- 

-    4  = 

iof    6  = 

14-9  = 

4- 

-   4  = 

iof    8  = 

14-5  = 

12- 

-    3  = 

^  of  10  = 

14  -  10  = 

3- 

-    3  = 

1  of  12  = 

8  +       =14. 

14- 

—       = 

5. 

12^       =2 

9  +       =14. 

14- 

=-      = 

7. 

12  ^-       =1 

10  +       =  14. 

7> 

<       = 

14. 

iof       =1 

14  -       =    6.  . 

12- 

H           = 

6. 

iof       =6 

14-       =8. 

12- 

= 

4. 

iof       =2 

14-       =    4. 

12- 

= 

3. 

iof       =5 

14  -       =  10. 

12- 

= 

6. 

iof       =3 

14-       =9. 

12- 

= 

12. 

iof       =4 

12  inches  = 

1  fool 

=       inches. 

6  inches  := 

iofa 

I  foot 

=        inches. 

272  FIRST   STEPS  IN   NUMBER. 

If  I  have  eight  apples,  and  you  have  six  apples,  how 
many  apples  must  I  give  you  that  we  may  each  have  the 
same  number  of  apples?  If  I  give  you  one  apple,  how 
many  will  you  have  ?  How  many  shall  I  have  ?  How 
many  shall  we  have  altogether  ?  What  two  equal  numbers 
have  you  just  found  make  fourteen  ? 

Seven  days  and  seven  days  are  how  many  days  ?  Two 
weeks  are  how  many  days  ? 

Two  poles,  each  seven  feet  long,  contain  how  many 
feet? 

There  are  two  groups  of  stars,  called  the  Great  Dipper 
and  the  Little  Dipper,  and  each  group  has  seven  stars  to 
form  the  dipper.  How  many  stars  are  there  in  both 
dippers? 

In  winter  the  days  are  only  about  seven  hours  long. 
How  many  hours  of  daylight  in  two  winter  days  ? 

Seven  bright  maples,  and  seven  dark  oaks,  are  how  many 
trees  ? 

Seven  humble-bees,  and  seven  morning-glories,  are  how 
many  blossoms  and  bees  together  ? 

Two  little  girls,  each  with  seven  daisies,  have  how  many 
blossoms?  If  seven  of  the  blossoms  fall  to  pieces,  how 
many  blossoms  will  remain  ? 

If  you  find  fourteen  pretty  shells  on  the  beach,  but  seven 
fade  and  are  no  longer  pretty,  how  many  pretty  shells  will 
you  have  ? 

If  seven  and  seven  make  fourteen,  how  many  sevens 
make  fourteen? 

Express  this  fact  on  the  board.     (2  X  7  =  14.) 

If  two  sevens  make  fourteen,  what  is  one-half  of  four- 
teen? 

Express  this  fact  on  the  board.    (^  of  14  is  7.) 

If  fourteen  is  divided  into  groups  of  seven  each,  how 
many  groups  will  be  found  ? 


THE  NUMBER  FOURTEEN.  273 

Express  this  fact  on  the  board.     (14  -^7  =  2.) 

Give  me  a  story  for  each  fact  you  have  expressed. 

A  boy  who  made  brackets  for  sale  had  fourteen  of  one 
design.  He  sold  seven  of  the  brackets  in  one  morning. 
How  many  had  he  left  ? 

Nellie  is  fourteen  years  old.  How  old  was  she  when  she 
was  only  half  as  old  as  she  is  now  ? 

If  I  can  ride  fourteen  miles  on  my  car-ticket,  and  I  use 
half  of  my  ticket,  how  many  miles  do  I  ride  ? 

If  there  are  fourteen  weeks  in  one  term  of  the  school, 
how  many  weeks  in  one-half  a  term  ? 

If  there  are  fourteen  chairs  in  a  row,  how  many  chairs 
in  half  of  the  row? 

In  fourteen  days  how  many  weeks  ? 

How  many  seven-cent  books  can  be  bought  for  fourteen 
cents  ? 

How  many  sticks,  each  seven  feet  long,  can  be  cut  from 
a  pole  fourteen  feet  long  ? 

If  it  takes  seven  buttons  for  each  jacket,  how  many  jack- 
ets will  fourteen  buttons  supply  ? 

A  lady  who  has  fourteen  geranium  blossoms  arranged 
them  in  groups  of  seven  each.  How  many  groups  did 
she  form  ? 

Fill  out  the  blanks  in  these  expressions : 


7+    7  = 

10  + 

4 

= 

14^ 

=   2. 

2x    7  = 

14^ 

2 

= 

8  + 

=  14. 

i  of  14  = 

7x 

2 

= 

5  + 

=  14. 

14-^-7  = 

7  + 

=  14. 

4  + 

=  14. 

8+    6  = 

2x 

=  14. 

14  ^- 

=    7. 

9+    5  = 

iof 

=    7. 

7x 

=  14. 

6+    8  = 

14-^ 

=  14. 

9  + 

=  14. 

5+    9  = 

14-*- 

=    1. 

6  + 

=  14. 

274  FIRST  STEPS   IN  NUMBER. 

Exercise  for  Review. 

If  it  is  three  times  as  far  round  a  wheel  as  across  it,  how 
far  is  it  round  a  wheel  that  is  four  feet  across?  that  is  three 
feet  across  ? 

If  a  circle  is  three  inches  across,  how  many  inches  is  the 
circle  round  the  outside  ? 

If  a  circle  is  four  inches  across,  how  far  is  it  round  the 
outside  of  the  circle  ? 

If  a  circle  is  six  inches  round  the  outside,  how  far  is  it 
across  the  circle  ? 

If  a  wheel  is  nine  inches  round  the  outside,  how  far  is  it 
across  the  wheel  ? 

If  a  wheel  is  twelve  inches  round  the  outside,  how  far  is 
it  across  the  wheel  ? 

How  many  inches  long  is  a  stick  that  is  one-half  of  a 
foot? 

My  penholder  is  half  of  a  foot  and  three  inches  long. 
How  long  is  my  penholder  ? 

My  pencil  is  one-fourth  of  a  foot  long.  How  many  inches 
in  length  is  my  pencil  ? 

If  the  cook  uses  one-fourth  of  a  dozen  eggs  for  a  custard- 
pudding,  how  many  eggs  does  she  use  ? 

If  I  distribute  a  dozen  cookies  equally  among  four  chil- 
dren, how  many  cookies  shall  I  give  to  each  ? 

It  takes  a  dozen  months  to  make  a  year.  How  many 
months  are  there  in  one-fourth  of  a  year  ? 

The  year  is  divided  into  four  seasons.  Each  season  has 
the  same  number  of  months.  How  many  months  has  each 
season  ?  Each  season  is  what  part  of  a  year  ?  How  many 
autumn  months  are  there  ?     How  many  spring  months  ? 

If  each  letter  requires  a  two-cent  stamp,  how  much  will 
it  cost  to  send  seven  letters  ?  Fourteen  cents  will  buy  how 
many  two-cent  stamps  ? 


THE  NUMBER  FOURTEEN.  275 

A  large  milk-pail  holds  a  dozen  quarts.  How  many  two- 
quart  pails  of  milk  does  it  hold  ?  How  many  three-quart 
pails  of  milk  ?  How  many  four-quart  pails  of  milk  ?  How 
many  six-quart  pails  of  milk  ?  If  a  six-quart  pail  of  milk 
be  emptied  into  it,  how  nearly  full  will  it  be  ?  If  a  four- 
quart  pail  of  milk  be  emptied  into  it,  how  nearly  full  will 
it  be?     If  a  three-quart  pail  of  milk  be  emptied  into  it? 

Fourteen  ink-wells  will  supply  how  many  inkstands,  if 
each  inkstand  has  two  wells  ? 

I  have  a  square  box  whose  edge  is  seven  inches.  How 
many  inches  is  it  half-way  round  the  box?  This  box  is 
twice  as  deep  as  it  is  broad.     How  deep  is  it  ? 

Harry  picked  ten  quarts  of  blueberries  and  four  quarts 
of  huckleberries.  He  sold  half  of  his  berries.  How  many 
quarts  did  he  sell  ? 

If  note-paper  is  seven  cents  a  quire,  how  much  will  two 
quires  cost? 

For  fourteen  cents,  how  many  bunches  of  envelopes,  at 
seven  cents  a  bunch,  can  you  buy  ? 

How  many  lines,  an  inch  apart,  and  each  two  inches  long, 
can  Mary  make  across  a  page,  if  the  page  is  six  inches 
across  ?  If  the  page  is  nine  inches  across  ?  If  the  page  is 
twelve  inches  across  ? 

The  rails  in  a  fence  are  three  inches  wide,  and  are  placed 
three  inches  apart.  How  many  rails  are  there  in  a  foot  of 
the  fence  ?  In  two  feet  of  the  fence  ?  In  three  feet  of  the 
fence  ?    In  seven  feet  of  the  fence  ? 

If  I  draw  as  large  a  circle  as  I  can  in  a  square  that  is 
three  inches  on  a  side,  how  many  inches  across  will  the 
circle  be  ?  How  many  inches  round  the  circle  ?  How 
many  more  inches  round  the  square  than  round  the  circle  ? 

I  bought  nine  yards  of  woollen  goods,  and  five  yards  of 
silk  goods.  When  I  had  used  six  yards  of  the  material,  how 
many  yards  had  I  left  ? 


276  FIRST  STEPS   IN   NUMBER. 

Into  how  many  pieces  shall  I  cut  a  strip  of  paper,  if  I  cut 
through  it  twice?  If  I  cut  it  three  times?  If  I  cut  it 
eight  times  ?  If  I  cut  it  twelve  times  ?  If  I  cut  it  thirteen 
times  ? 

Into  how  many  pieces  does  a  man  saw  a  stick  of  wood,  if 
he  saws  through  the  stick  twice  ?  If  he  saws  through  the 
stick  three  times  ?     If  he  saws  through  the  stick  once  ? 

How  many  working  days  in  a  week  and  five  days  ? 

How  many  Sundays  in  thirteen  days,  beginning  with 
Monday  ?  How  many  Tuesdays  ?  How  many  Fridays  ? 
How  many  Saturdays  ? 

If  I  make  a  book  by  folding  a  piece  of  paper  once,  how 
many  pages  will  the  book  have  ?  If  I  fold  the  paper  twice, 
how  many  pages  will  the  book  have  ?  If  I  fold  the  paper 
three  times,  how  many  leaves  will  the  book  have  ? 

See  how  many  different  arrangements  you  can  make  of 
the  figures  1,  2,  and  3. 

Here  is  a  button  that  is  two  inches  round.  I  will  chalk 
the  edge,  and  you  may  roll  it  round  once  on  the  board. 
How  long  is  the  line  it  marks  ? 

Here  is  a  circle  that  is  six  inches  round.  Mark  its  edge 
with  chalk,  and  roll  it  once  round  on  the  board.  How  long 
is  the  line  which  it  marks  ? 

Annie  has  a  hoop  that  is  five  feet  round.  How  many 
feet  of  ground  will  it  go  over  in  turning  round  twice  ? 

A  wheel  that  is  two  yards  round  will  go  over  how  many 
yards  in  turning  round  seven  times?  In  turning  round 
five  times  and  half  round  again?  In  turning  six  and  a 
haK  times  round  ? 

How  long  a  time  is  it  from  twelve  o'clock  at  noon  to  eight 
o'clock  in  the  evening?  From  one  o'clock  to  eight  o'clock? 
From  eight  o'clock  in  the  morning  to  six  o'clock  in  the 
evening?  From  six  o'clock  in  the  morning  to  eight  o'clock 
in  the  evening? 


THE   NUMBER  FOURTEEN.  277 

The  short  hand  goes  round  the  face  of  the  clock  only 
once  while  the  long  hand  is  going  round  twelve  times. 
When  the  short  hand  has  gone  half-way  round  the  clock, 
how  many  times  has  the  long  hand  been  round  the  clock  ? 
When  the  short  hand  has  been  a  fourth  round  the  clock,  how 
many  times  has  the  long  hand  been  round  the  clock  ?  When 
the  short  hand  has  been  a  third  round  the  clock,  how  many 
times  has  the  long  hand  been  round  ? 

What  time  is  it  when  the  long  hand  points  directly  up- 
ward, and  the  short  hand  in  the  opposite  direction  ?  When 
it  is  five  minutes  past  the  hour,  at  what  figure  does  the 
long  hand  point  ?  When  it  is  ten  minutes  past  the  hour  ? 
When  it  is  five  minutes  of  the  hour  ? 

The  outside  of  a  square  flower-border  was  three  feet  on  a 
side  ;  the  inside  was  two  feet  on  a  side.  How  much  farther 
round  was  it  on  the  outside  than  on  the  inside  ? 

We  will  do  some  buying  and  selling  to-day.  George  may 
be  salesman,  and  set  his  own  price  on  the  goods  he  sells, 
but  must  not  charge  more  than  twelve  cents  for  any  article, 
as  I  shall  not  send  any  children  to  the  store  with  more  than 
twelve  cents.  Look  over  the  goods  and  tell  me  what  there 
is  to  sell.  [Boxes  of  matches,  thimbles  (clay),  marbles  (clay), 
spools  of  thread  (empty  spools),  lozenges  (pasteboard  disks), 
sticks  of  candy  (colored  sticks),  pencils,  papers  of  pins,  pa- 
pers of  needles,  pinballs,  apples,  pears,  plums,  grapes, 
peaches,  oranges  (clay),  hat-pins  (splints),  pens,  toy  matches, 
toy  tools  (paper),  postage-stamps,  pictures,  cards,  sand- 
paper, blotting-paper,  tissue-paper,  narrow  ribbon,  narrow 
lace,  newspapers,  envelopes,  star-books,  pencil-tablets.] 

Teacher.  Nellie  may  run  to  the  store  and  buy  a  thimble 
for  herself  and  a  paper  of  No.  10  needles  for  me.  (She 
is  given  a  ten-cent  piece.) 

Nellie  at  the  store.  I  wish  for  a  thimble  for  myself  and  a 
paper  of  No.  10  needles. 


278  FIRST  STEPS   IN   NUMBER. 

Salesman,  Tliimble  two  cents,  needles  five  cents,  and 
three  cents  are  ten  cents. 

T.    Tell  me  about  your  purchase,  Nellie. 

Frank  may  buy  a  small  bottle  of  ink  and  a  half  dozen 
pens.  (Frank  is  given  a  five-cent  piece  and  two  three-cent 
pieces.) 

Franlc.    I  wish  for  a  bottle  of  ink  and  a  half  dozen  pens. 

S.  Bottle  of  ink  five  cents,  pens  five  cents,  and  one  cent 
are  eleven  cents. 

Harry  may  buy  two  sheets  of  coarse  sand-paper  and 
this  morning's  paper.  (Harry  is  given  a  five-cent  piece 
and  two  two-cent  pieces.) 

8,  Two  sheets  of  sand-paper  four  cents,  and  the  news- 
paper three  cents,  and  two  cents  are  nine  cents. 

T.  Annie  may  buy  three  two-cent  postage-stamps  and 
two  sheets  of  white  tissue-paper.  (Annie  is  given  four  three- 
cent  pieces.) 

8.  Three  two-cent  stamps  six  cents,  two  sheets  of  tissue- 
paper  four  cents,  and  two  cents  are  twelve  cents. 

T.  Cyrus  may  be  salesman.  Willie  may  buy  a  half 
dozen  apples  and  three  peaches.  (Willie  is  given  two  threes 
and  a  five.) 

8.  Six  apples  three  cents,  three  peaches  six  cents,  and 
two  cents  are  eleven  cents. 

T.  Nettie  may  buy  what  she  wishes  to  buy,  and  tell  me 
about  it  afterwards.     (Nettie  is  given  some  money.) 

T.  Henry  may  buy  anything  he  wants,  and  tell  me 
about  it  afterwards. 

T.  Joe  may  buy  two  sticks  of  candy  and  a  watch.  Tell 
me  about  the  purchase  when  you  return. 

This  exercise  will  require  some  tact  on  the  teacher's  part  at  first, 
that  it  may  run  smoothly  ;  hut  after  a  few  exercises  the  children 
will  price  the  goods  very  fairly,  and  count  out  change  in  a  businesfl- 


THE  NUMBER  FOURTEEN.  279 

like  way.  A  dollar  in  small  pieces  of  money  will  be  sufficient.  The 
salesman  needs  a  few  cents  to  begin  the  sales.  The  rest  of  the  money 
is  spent  by  the  customers.  The  exercise  tests  the  children's  power 
to  apply  their  knowledge  of  number,  acquaints  them  with  prices  of 
small  articles,  and  gives  practice  in  handling  money. 

Ten  and  one  are  how  many  ? 

Ten  and  two  are  how  many  ? 

Ten  and  three  are  how  many  ? 

Ten  and  four  are  how  many  ? 

Nine  and  five  are  how  many  ? 

Nine  and  four  are  how  many  ? 

Nine  and  three  are  how  many  ? 

Nine  and  two  are  how  many  ? 

Eight  and  how  many  are  fourteen  ? 

Eight  and  how  many  are  twelve  ? 

Eight  and  how  many  are  ten  ? 

Eight  and  how  many  are  thirteen  ? 

Eight  and  how  many  are  eleven? 

What  number  and  seven  are  fourteen? 

What  number  and  four  are  eleven  ? 

What  number  and  seven  are  thirteen  ? 

What  number  and  five  are  twelve  ? 

What  number  and  seven  are  ten  ? 

Express  on  the  board  the  sum  of  any  two  numbers  that 
together  make  fourteen ;  that  together  make  ten  ;  that  to- 
gether make  thirteen ;  that  together  make  eleven. 

Fill  out  these  blanks  : 


2x    7  = 

6x2  = 

12h-   4 

7x   2  = 

12 --6  = 

J  of  12 

14^-   7  = 

12 --2  = 

iof  12 

14^   2  = 

3x4  = 

J  of  12 

J  of  14  = 

4x3  = 

4  gills 

2x   6  = 

12^3  = 

2  pints 

280  FIRST   STEPS   IN   NUMBER. 

12  inches  =  2  weeks      =  ^  of  a  pint    = 

12  things  =  3  months    =.  ^  of  a  quart  = 

7  days      =  ^-  of  a  foot  =  ^  of  a  year    = 

12  months  =  ^  of  a  foot  =  I-  of  a  dozen  = 

4  weeks   =  -|^  of  a  foot  —  -J-  of  a  week  = 

The  Yard. 

Here  is  the  longest  measure  you  have  yet  seen.  Some  of 
you  are  not  as  tall  as  this  stick,  when  I  stand  it  up.  Who 
knows  how  long  this  stick  is  ?  It  is  a  yard  long.  Who  has 
seen  a  yard-stick  at  home  ?  Who  has  seen  anybody  measure 
with  such  a  stick  ?  What  did  you  see  measured  ?  Who  has 
seen  a  yard-measure  that  was  not  a  stick  ?  You  may  each 
take  one  of  these  long  strips  of  paper.  How  long  do  you 
think  each  is?  Draw  a  line  on  the  board  a  yard  long. 
Measure  off  a  yard  on  this  edge  of  the  table  ;  on  the  edge 
of  the  platform ;  on  the  seat  of  the  settee  ;  on  the  back  of 
the  settee ;  on  the  edge  of  the  blackboard ;  on  the  edge 
of  the  door ;  on  the  floor ;  on  the  window-frame ;  on  the 
blind.  What  do  you  see  in  this  room  that  you  think  is  a 
yard  long?  What  have  you  seen  at  home  that  is  a  yard 
long  ?  Tell  me  to-morrow  how  wide  each  strip  of  carpet  is 
that  covers  the  floor  of  your  room.  Where  have  you  seen 
a  yard-stick  used  in  measuring  a  great  many  things  ?  What 
is  bought  by  the  yard  ? 

Feet  in  a  Yard. 

Nettie  may  put  her  foot-rule  on  this  yard-stick.  Which 
is  the  longer  measure  ? 

Charley  may  put  his  foot-rule  on  the  yard-stick,  right 
against  Nettie's.  Are  the  two  rules  together  as  long  as  the 
yard-stick  ? 


THE   NUMBER   FOURTEEN.  281 

Mary  may  put  her  foot-rule  right  against  Charley's.  Are 
the  three  foot-rules  together  as  long  as  the  yard-stick? 

Show  me  one  foot  on  the  yard-stick ;  another ;  another. 

How  many  have  you  shown  me  ?  How  many  feet  then 
make  a  yard  ? 

Mabel,  see  if  there  are  three  feet  in  a  yard. 

I  have  some  lines  on  the  board.  Find  how  long  each  is. 
(Three  feet.) 

Tell  me  in  two  ways  how  long  the  line  is.  (Three  feet ; 
a  yard.) 

This  table  is  a  yard  wide.  Find  how  many  feet  wide  the 
table  is. 

The  window-sill  is  a  yard  long.  Find  how  many  feet 
long  the  window-sill  is. 

This  part  of  the  blind  is  a  yard  high.  How  many  feet 
high  is  it  ? 

From  this  crack  in  the  floor  to  this  crack  in  the  floor  is 
a  yard.     How  many  feet  between  these  two  cracks  ? 

If  the  carpet  is  a  yard  wide,  how  many  feet  wide  is  it  ? 

If  Susie  is  just  a  yard  in  height,  how  many  feet  tall  is 
Susie? 

The  baby  is  two  feet  tall,  and  George  is  a  yard  in  height. 
Which  is  the  taller? 

If  this  platform  is  twelve  feet  across,  how  many  yards 
across  is  it  ? 

If  this  table  is  six  feet  long,  how  many  yards  long  is  it  ? 

If  a  room  is  nine  feet  high,  how  many  yards  high  is  it  ? 

What  part  of  a  yard  is  twelve  inches  ? 

Write  on  the  board  :  3  feet  =  1  yard. 


CHAPTER  XV. 

THE  NUMBER   FIFTEEN. 


§  37.   The  Number  Fifteen. 

Show  me  fourteen  with  the  tens  and  ones.  Put  one  more 
with  fourteen.     How  many  more  than  ten  have  you  now? 

Ten  and  five  are  how  many  ? 

Put  your  splints  back.  Take  fifteen  again.  How  many 
tens  have  you  taken?     How  many  ones  besides? 

Write  in  words :  One  ten  and  five  are  fifteen. 

Who  can  express  this  new  number  in  figures  ? 

For  what  does  the  figure  1  stand  ?  the  figure  5  ? 

Write  all  the  numbers  as  far  as  fifteen  that  are  expressed 
by  two  figures.     How  many  tens  in  each  of  these  numbers? 

Which  has  the  greatest  number  of  ones  besides  the  one 
ten? 

Which  has  the  least  number  of  ones  besides  the  one  ten  ? 

Fifteen  is  how  many  more  than  ten  ? 

A  ten-cent  piece  and  a  five-cent  piece  are  how  much 
money? 

A  ten-foot  pole  and  a  five-foot  pole  contain  how  many 
feet  ? 

My  ten  fingers  and  five  of  your  fingers  are  how  many 
fingers  ? 

If  it  is  ten  miles  to  my  home,  how  many  miles  is  it  there 
and  half-way  back  ? 


THE   NUMBER  FIFTEEN.  283 

If  a  yard  of  cloth  costs  ten  cents,  what  will  a  yard  and  a 
half  cost  ? 

If  a  hall  is  ten  feet  long  and  five  feet  wide,  how  many 
feet  are  in  the  length  and  the  width  together? 

What  two  pieces  of  money  make  fifteen  cents  ? 

What  two  pieces  of  money  make  fifteen  dollars  ? 

If  there  are  fifteen  splints  before  me  on  the  table,  and  I 
take  five  of  the  splints,  how  many  splints  remain  ? 

If  you  have  fifteen  more  days  to  go  to  school,  how  many 
days  will  you  have  to  go  after  you  have  been  five  days  ? 

Fifteen  minus  five  are  how  many  ? 

Express  this  fact  on  the  board. 

Who  has  an  example  for  fifteen  minus  five  ? 

Who  can  tell  me  what  fifteen  minus  ten  will  leave  ? 

If  I  have  fifteen  cents,  and  buy  a  ten-cent  loaf  of  bread, 
how  many  cents  shall  I  have  left  ? 

My  pencil-tray  is  fifteen  inches  in  length  and  width  to- 
gether.    Its  length  is  ten  inches ;  what  is  its  width  ? 

If  there  are  fifteen  bananas  in  a  bunch,  and  ten  are  sold, 
how  many  bananas  are  in  the  bunch  ? 

Express  fifteen  minus  ten  on  the  board. 

Show  me  fifteen,  using  a  bundle  of  ten  splints. 

Now  I  want  to  find  how  many  fives  in  fifteen. 

In  ten  how  many  fives  ?  and  one  more  five  will  make  how 
many  fives? 

In  ten  and  five,  then,  how  many  fives  ? 

In  fifteen  how  many  fives? 

How  many  five-cent  whistles  can  I  buy  for  fifteen  cents  ? 

How  many  five-cent  postage-stamps  can  I  buy  for  fifteen 
cents  ? 

If  I  have  fifteen  walnuts,  to  how  many  boys  can  I  give 
five  apiece? 

If  you  arrange  fifteen  dots  on  the  board  in  rows  of  five 
each,  how  many  rows  will  you  make  ? 


284  FIRST  STEPS   IN   NUMBER. 

Fifteen  divided  by  five  are  how  many  ? 

Express  this  fact  on  the  board  a  half  dozen  times. 

Give  an  example  for  what  you  have  expressed. 

If  fifteen  divided  by  five  are  three,  how  many  fives  make 
fifteen  ? 

Three  five-dollar  gold  pieces  are  how  many  dollars  ? 

Three  five-cent  pieces  of  money  are  how  many  cents  ? 

Three  five-cent  pencils  cost  how  many  cents  ? 

You  are  in  school  five  days  a  week.  How  many  days 
are  you  in  school  in  three  weeks  ? 

A  pansy-blossom  has  five  petals.  How  many  petals  have 
three  pansy-blossoms  ? 

Three  fives  are  how  many  ? 

Express  this  fact  five  times. 

Give  an  example  for  what  you  have  expressed. 

If  you  divide  fifteen  into  three  equal  parts,  how  many 
will  there  be  in  each  part  ?  What  then  is  one-third  of 
fifteen  ? 

A  farmer  who  had  fifteen  sheep,  sold  one-third  of  his 
flock.     How  many  sheep  did  he  sell  ? 

There  were  fifteen  children  in  a  class,  but  one  stormy 
day  one-third  of  the  class  was  absent.  How  many  children 
were  absent? 

A  farmer  bought  fifteen  hens.  One-third  of  the  number 
was  jet  black.     How  many  were  black  ? 

One-third  of  fifteen  is  how  many? 

Express  this  fact. 

Give  an  example  for  what  you  have  expressed. 

Supply  the  term  that  is  needed  to  complete  these  expres- 
sions : 

10+5=  15-10=  I  of  15  = 

15-5=  15-^    5=  10+       =15. 

5  +  10=  3x5=  5+       =15. 


THE   NUMBER  FIFTEEN  285 


15^ 

=    3. 

+    5  =  15. 

-10=    5. 

iof 

=    5. 

X    5  =  15. 

+  10  =  15. 

3x 

=  15. 

-^    5=    3. 

+  14  =  15. 

15- 

=    5. 

•-    5  =  10. 

+  13  =  15. 

15- 

=  10. 

of  15=    5. 

+  12  =  15. 

James  had  ten  nuts.  Harry  had  five  nuts.  How  many- 
did  both  have  ? 

James  gave  one  of  his  nuts  to  Harry.  How  many  nuts 
did  each  have  then?     How  many  did  both  have? 

Nine  nuts  and  six  nuts  are  how  many  nuts  ? 

If  there  are  nine  biscuits  on  one  tea-plate  and  six  on 
another,  how  many  biscuits  are  on  both  plates? 

If  the  distance  is  nine  miles  from  one  station  to  another, 
and  six  miles  to  the  next  station,  how  many  miles  is  it  from 
the  first  station  to  the  third  ? 

Give  me  an  example  for  nine  and  six.  Express  the  fact 
on  the  board. 

Give  an  example  for  fifteen  minus  six. 

Give  an  example  for  fifteen  minus  nine. 

Nine  and  how  many  are  fifteen  ? 

Six  and  how  many  are  fifteen  ? 

Fifteen  minus  how  many  are  nine  ? 

Express  this  fact  on  the  board. 

Fifteen  minus  how  many  are  six  ? 

Express  this  fact  on  the  board. 

I  want  to  find  how  many  threes  there  are  in  fifteen.  I 
wonder  who  will  think  it  out.  Think  how  many  threes  in 
nine,  then  think  how  many  threes  in  six.  How  many  threes 
are  in  nine  and  in  six  together  ?  Then  how  many  threes 
are  in  fifteen  ? 

Fifteen  divided  by  three  are  how  many  ? 

There  are  fifteen  panes  of  glass  in  a  window,  three  panes 
in  each  row.     How  many  rows  of  panes  in  the  window  ? 


286  FIRST  STEPS   IN   NUMBER. 

Fifteen  cents  will  buy  how  many  three-cent  lead  pencils  ? 
how  many  three-cent  stamps  ?  how  many  three-cent  rubbers  ? 
how  many  three-cent  newspapers  ? 

Tell  me  a  story  for  fifteen  divided  by  three. 

Express  the  fact  on  the  board. 

Since  fifteen  divided  by  three  are  five,  how  many  threes 
make  fifteen  ? 

If  I  have  five  three-cent  pieces  of  money,  how  much 
money  have  I  ? 

A  spider-wort  blossom  has  three  petals.  How  many 
petals  have  five  spider-wort  blossoms? 

A  lady  is  going  to  make  some  dresses  for  five  little  girls, 
and  it  will  take  three  yards  of  cloth  for  each  dress.  How 
Tuany  yards  of  cloth  will  she  need  for  all  the  dresses  ? 

If  it  takes  three  yards  of  ribbon  to  trim  each  hat,  how 
many  yards  of  ribbon  are  needed  to  trim  five  hats  ? 

Give  an  example  for  five  threes  are  fifteen. 

What  five  equal  numbers  make  fifteen  ? 

What  three  equal  numbers  make  fifteen  ? 

Five  triangles  have  how  many  sides  ?  how  many  corners  ? 

How  many  toes  has  a  dog  on  three  feet  ? 

How  many  feet  in  five  yards  of  string? 

How  many  ounces  will  three  books  weigh,  each  of  which 
weighs  five  ounces?  How  many  ounces  will  five  books 
weigh,  each  of  which  weighs  three  ounces  ? 

Supply  the  missing  term  in  these  expressions : 


9+    6  = 

3x5  = 

^    3=    5. 

15-6  = 

15-^    5  = 

-    9=    6. 

15-9  = 

iofl5  = 

-    6  =    9. 

6+    9  = 

15  -  10  = 

10  +       --=  15. 

15-4-3  = 

X    3  = 

15. 

3  X       =15. 

5x    3  = 

+    9  = 

15. 

15^       =3. 

10 -f    5  = 

+    6  = 

15. 

iof      =5. 

THE   NUMBER  FIFTEEN.  287 

The  boys  chose  sides  in  playing  ball.  If  there  were  nine 
boys  on  one  side  and  six  boys  on  the  other  side,  how  many 
boys  were  playing  ?  If  one  from  the  larger  side  should  go 
to  the  other  side,  how  many  boys  would  there  be  on  each 
side  ?  and  how  many  in  all  ? 

Eight  and  seven  are  how  many  ? 

Who  thinks  of  an  example  for  this  fact  ? 

Express  the  fact  on  the  board. 

What  two  numbers  make  fifteen,  one  of  which  is  ten  ? 
one  of  which  is  nine  ?  one  of  which  is  eight  ?  one  of  which 
is  seven  ?  one  of  which  is  six  ?  one  of  which  is  five  ? 

What  three  equal  numbers  make  fifteen  ? 

What  five  equal  numbers  make  fifteen  ? 

Express  the  examples  I  give  you  on  the  board : 

[It  is  expected  that  the  pupil  will  express  the  operation  and  answer 
by  means  of  figures  and  signs  of  operations.] 

There  were  fifteen  chickens  roosting  on  a  fence,  and  nine 
flew  down.     How  many  were  left  on  the  fence? 

There  were  fifteen  jelly-fish  on  the  beach,  but  ten  of  them 
melted  in  the  sun.     How  many  were  left  ? 

A  star-fish  has  five  arms  or  rays.  How  many  rays  have 
three  star-fish  ? 

A  clover  leaf  has  three  parts.  How  many  parts  have 
five  clover  leaves? 

When  peaches  are  three  cents  apiece,  how  many  can  be 
bought  for  fifteen  cents? 

If  I  have  fifteen  cents  in  three  equal  pieces  of  money, 
what  is  each  piece  of  money  ? 

If  I  have  fifteen  cents  in  five  equal  pieces  of  money,  what 
is  each  piece  of  money  ? 

A  fence  is  seven  feet  long  one  side  of  the  gate  and  one 
foot  longer  on  the  other  side  of  the  gate.  How  long  is  the 
fence  besides  the  gate  ? 


288  FIEST  STEPS   IN  NUMBEK. 

Four  and  five  and  six  are  how  many  ? 

You  may  express  this  on  the  board. 

Seven  and  three  and  five  are  how  many  ? 

Express  this  on  the  board. 

Five  and  three  and  seven  are  how  many  ? 

Express  this  on  the  board. 

I  will  express  these  examples  a  new  way. 

[Let  teacher  express  in  a  vertical  column  with  the  answer  under- 
neath.] . 

Express  four  and  two  and  five  the  new  way. 

Express  five  and  six  and  two. 

Express  three  and  four  and  five  and  two. 

Express  one,  two,  three,  four,  and  five. 

Express  three,  two,  and  ten. 

Express  one,  two,  and  twelve. 

Take  this  number-work 
10+5=  7  +  7=  4  +  3=  15-3  = 


10  +  4  = 

7  +  2  = 

2x2  = 

15^5 

10  +  3  = 

7  +  6  = 

2x7  = 

14 -h- 2 

10  +  2  = 

7  +  3  = 

2x3  = 

14^7 

10  +  1  = 

7  +  5  = 

2x6  = 

12^2 

10  +  0  = 

7  +  4  = 

2x4  = 

12-^3 

9  +  6  = 

6  +  5  = 

2x5  = 

12 --4 

9  +  2  = 

6  +  2  = 

3x2  = 

12^6 

9  +  5  = 

6  +  4  = 

3x3  = 

10^2 

9  +  3  = 

6  +  3  = 

3x4  = 

10-^5 

9  +  4  = 

6  +  6  = 

3x5  = 

9^3 

.8  +  2  = 

6  +  5  = 

4x2  = 

8^2 

8+7  = 

5  +  2  = 

4x3  = 

8-^4 

8  +  3  = 

5  +  4  = 

5x2  = 

6-^2 

8  +  6  = 

5  +  8  = 

5x3  = 

6^3 

8  +  4  = 

4  +  4  = 

6x2  = 

iofl4 

8  +  5  = 

4  +  2  = 

7x2  = 

|of  12 

THE   NUMBER   FIFTEEN.  289 


1  of  10  = 

iof    1  = 

2  pints 

= 

2 

4 

i  of    8  = 

iof    0  = 

12  inches  = 

4 

3 

iof    6  = 

iof    8  = 

3  feet 

= 

3 

2 

iof    4  = 

i  of  15  = 

12  thing! 

3  = 

4 

1 

iof    2  = 

iof  12  = 

— 

— 

iof    1  = 

iof    9  = 

iof    0  = 

iof    6  = 

3 

1 

2 

2 

i  of  12  = 

iof    3  = 

2 

o 

5 

3 

iof    8  = 

4  gills    = 

4 

3 

3 

4 

iof   4  = 

The 

6 
Gallon. 

4 

4 

5 

Who  has  heard  any  one  speak  of  a  gallon  of  molasses  ?  a 
gallon  of  oil  ?  a  gallon  of  syrup  ? 

I  hold  in  my  hand  a  measure  that  holds  just  a  gallon. 

Who  has  seen  such  a  measure  before  ? 

Who  has  anything  at  home  that  holds  just  a  gallon? 

Who  has  heard  of  a  gallon-jug?  a  gallon-can? 

Which  holds  more,  this  quart  or  this  gallon  measure  ? 

You  may  find  how  many  quarts  a  gallon  will  hold. 

How  many  quarts  in  a  gallon  ? 

In  a  gallon  of  vinegar,  how  many  quarts  of  vinegar  ? 

If  I  buy  a  gallon  of  molasses,  how  many  quarts  do  I  buy  ? 

In  half  a  gallon  of  oil,  how  many  quarts  of  oil  ? 

In  a  half-gallon  of  ink,  how  many  quarts  of  ink  ? 

How  many  two-quart  pails  are  required  to  hold  a  gallon  ? 

How  many  pint  pails  are  required  to  hold  a  gallon  ? 

If  a  pint  of  water  weighs  one  pound,  how  much  will  a 
gallon  of  water  weigh  ? 

How  many  quarts  make  a  gallon  ? 

Write  on  the  board  :  4  quarts  ~  1  gallon. 


CHAPTER  XVI. 

THE    NUMBER    SIXTEEN. 


§  38.   The  Number  Sixteen. 

Take  ten  splints.  Take  six  more  splints.  What  number 
of  splints  kave  you  ? 

Ten  and  six  are  how  many? 

"Who  can  write  the  word  sixteen  f 

Who  can  express  sixteen  in  figures  ? 

How  many  tens  in  sixteen  ?     How  many  ones  beside  ? 

Which  figure  stands  for  the  one  ten  ? 

Which  figure  shows  that  there  are  six  ones  besides  the 
ten  in  sixteen  ? 

Express  all  the  numbers  that  contain  only  one  ten. 

Which  is  the  largest  number  you  have  expressed  ?  Which 
is  the  smallest  ? 

A  ten-cent  piece  of  money  and  two  three-cent  pieces  of 
money  are  how  much  money  ? 

A  ten-cent  piece  of  money  and  three  two-cent  pieces  of 
money  are  how  much  money  ? 

Two  five-cent  pieces  of  money  and  two  three-cent  pieces 
of  money  are  how  much  money  ? 

If  one  keg  holds  ten  gallons  of  cider-apple  sauce,  and 
another  keg  holds  six  gallons,  how  many  gallons  will  both 
kegs  hold  together  ? 

There  were  sixteen  boys  in  a  class,  but  six  were  promoted 
to  another  grade.     How  many  boys  were  left  in  the  class  ? 


THE   NUMBER  SIXTEEN.  291 

There  were  sixteen  swallows'  nests  in  a  bank,  but  tbe  bank 
caved  in  and  destroyed  six  nests.  How  many  nests  were 
then  in  the  bank  ? 

Sixteen  boys  were  playing  ball,  but  ten  ran  home  to 
dinner.     How  many  boys  were  then  playing  ball  ? 

Sixteen  crows  alighted  in  a  corn-field.  Two  of  them  were 
frightened  away  by  the  flapping  garments  of  an  old  scare- 
crow, but  the  rest  did  not  care  a  fig.  How  many  stayed 
and  ate  the  corn  ? 

Ten  and  how  many  are  sixteen  ? 

Express  this  fact  on  the  board. 

Sixteen  minus  ten  are  how  many  ? 

Express  this  fact  on  the  board. 

Sixteen  minus  what  number  are  ten  ? 

Express  this  fact  on  the  board. 


If  you  take  a  splint  from  the  bundle  of  tens  and  put  it 
w^th  six,  what  two  numbers  will  you  then  have  ?  Ten  and 
six  are  how  many  ?     Nine  and  seven  are  how  many? 

Give  an  example  for  nine  and  seven. 

Express  this  fact  on  the  board. 

Give  an  example  for  sixteen  minus  nine. 

Express  this  fact  on  the  board. 

Give  an  example  for  sixteen  minus  seven. 

Express  this  fact  on  the  board. 

If  Henry  finds  nine  eggs  in  one  nest  and  seven  in  another 
nest,  how  many  eggs  does  he  find  in  all  ? 

In  two  pods  there  were  sixteen  peas.  If  there  were 
nine  peas  in  one  pod,  how  many  peas  were  in  the  other 
pod? 

Johnnie  was  peddling  chestnuts.  He  started  out  with 
sixteen  quarts,  and  sold  nine  quarts  within  half  an  hour. 
How  many  quarts  had  he  then  to  sell  ? 


292  FIRST  STEPS   IN  NUMBER. 

An  old  ladder  lay  in  the  loft  with  several  rounds  broken 
out.  It  had  sixteen  rounds  when  it  was  new ;  now  only 
seven  remained.     How  many  were  broken  ? 


Express  on  the  board :  Nine  and  seven  are  sixteen. 

If  you  take  one  from  nine,  what  number  will  remain  ? 

Express  eight  below  nine. 

Now  put  the  number  you  take  'from  nine  with  seven^  and 
what  number  will  you  have  ? 

Express  this  eight  below  seven. 

What  two  numbers  have  you  made  by  taking  one  from 
nine  and  adding  it  to  seven? 

What  must  be  the  sum  of  these  two  numbers  ? 

Express  this  fact. 

If  eight  and  eight  are  sixteen,  how  many  eights  are  in 
sixteen  ? 

Express  the  fact :  Sixteen  divided  by  eight  are  two. 

If  there  are  two  eights  in  sixteen,  how  many  eights  make 
sixteen  ? 

Express  the  fact :  Two  eights  are  sixteen. 

What  two  equal  numbers  have  you  found  then  in  sixteen  ? 
What  part  of  sixteen  must  each  of  the  numbers  be  ? 

What  then  is  one-half  of  sixteen  ? 

Express  the  fact :  One-half  of  sixteen  is  eight. 

If  two  eights  are  sixteen,  what  will  remain  if  one  eight  is 
taken  away? 

Sixteen  minus  eight  then  are  how  many  ? 

Express  this  fact. 

Read  the  facts  you  have  expressed. 

Illustrate  each  fact  by  drawings  on  the  board. 

A  flock  of  sheep  was  going  along  the  road.  Eight  were 
marked  with  black  spots  and  eight  were  white.  How 
many  sheep  were  in  the  flock  ? 


THE  NUMBER  SIXTEEN.  293 

Sixteen  fruit  trees  blossomed  in  our  orchard,  but  only- 
eight  bore  fruit.     How  many  did  not  bear  fruit  ? 

In  a  horse-car  there  were  eight  persons  on  each  side. 
How  many  persons  were  in  the  car  ? 

How  many  eight-cent  spools  of  silk  can  I  buy  for  sixteen 
cents  ? 

Two  boys  had  sixteen  small  pears  which  they  divided 
equally  between  themselves.     How  many  pears  had  each  ? 

If  I  ride  sixteen  miles,  but  you  ride  only  one-half  as  far, 
how  far  do  you  ride  ? 

Read  what  I  have  expressed  (8  +  8  =  16). 

What  two  equal  numbers  make  eight  ? 

Express  "  four  and  four  "  beneath  the  first  eight ;  beneath 
the  second  eight. 

Read  each  eight  in  fours. 

If  eight  and  eight  are  sixteen,  what  is  the  sum  of  four 
and  four  and  four  and  four?  How  many  fours?  Four 
fours  then  are  how  many  ? 

Express  :  Four  fours  are  sixteen. 

If  there  are  four  panes  of  glass  in  each  window,  how 
many  panes  of  glass  are  in  four  windows  ? 

Four  chairs  have  how  many  legs  together? 

Four  squares  have  how  many  sides  all  together?  have 
how  many  corners  ? 

If  one  quart  of  milk  costs  four  cents,  what  will  a  gallon 
of  milk  cost  ? 

If  four  fours  make  sixteen,  how  many  fours  can  be  taken 
from  sixteen?  Sixteen  divided  by  four  are  how  many 
then? 

Express  this  fact. 

Sixteen  quarts  of  milk  will  fill  how  many  gallon-cans  ? 

Sixteen  cents  will  buy  how  many  yards  of  ribbon  at  four 
cents  a  yard  ? 

Sixteen  horses  will  supply  how  many  four-horse  coaches? 


294  FIRST  STEPS   IN  NUMBER. 

Into  wliat  four  equal  numbers  can  sixteen  be  divided  ? 
What  part  of  sixteen  is  each  of  the  numbers? 

What  then  is  one-fourth  of  sixteen  ?     Express  this  fact. 

There  were  sixteen  empty  cars  on  a  freight  train  when  it 
started  from  the  station,  but  a  quarter  of  them  were  switched 
off  at  the  next  station.     How  many  cars  were  switched  off? 

A  summer  day  is  sixteen  hours  long.  How  long  is  a 
fourth  of  the  day  ? 

This  string  is  five  yards  and  a  foot  long.  How  many 
feet  long  is  one-fourth  of  the  string  ? 

Edwin  had  sixteen  hens  but  he  sold  four  hens.  What 
part  of  his  whole  number  of  hens  did  he  sell  ? 

Supply  the  missing  term  in  these  expressions : 


8+    8  = 

iofl6 

= 

4  gills 

= 

16-8  = 

16- 

=  10. 

2  pints 

= 

2x    8  = 

16- 

=    9. 

4  quarts 

= 

16-^    8  = 

16- 

=    8. 

12  inches 

= 

i  of  16  = 

10  + 

=  16. 

3  feet 

= 

10+6  = 

9  + 

=  16. 

12  things 

= 

16  -  10  = 

8  + 

=  16. 

16-6  = 

2x 

=  16. 

3 

2 

9+    7  = 

4x 

=  16. 

4 

4 

16-9  = 

16^ 

=    2. 

2 

3 

16-7  = 

16-^ 

=    4. 

3 

3 

4x4  = 

iof 

=    8. 

4 

3 

16^    4  = 

iof 

=    4. 

— 

— 

Read  what  I  have  written  (8  +  8  =  16). 

How  many  twos  make  eight?  What  then  is  just  the 
same  as  eight?  (4  X  2.) 

Express  two  and  two  and  two  and  two  under  each 
eight.  Read,  Eight  and  eight  are  sixteen,  by  twos  (2  +  2 
+  2+2  +  2  +  2  +  2  +  2  =  16).  How  many  twos? 
How  many  twos  make  sixteen  then  ? 


THE   NUMBER  SIXTEEN.  295 

Express:  Eight  twos  are  sixteen. 

If  eight  twos  make  sixteen,  into  how  many  twos  may 
sixteen  be  divided  ? 

Express :  Sixteen  divided  by  two  are  eight. 

How  many  pairs  of  gloves  in  sixteen  gloves  ? 

Ned  has  sixteen  cents  in  two-cent  pieces.  How  many 
two-cent  pieces  has  he  ? 

Eight  spans  of  horses  are  how  many  horses  ? 

Eight  yokes  of  oxen  are  how  many  oxen  ? 

Eight  birds  have  how  many  wings  ? 

What  eight  equal  numbers  make  sixteen  ?  What  part  of 
sixteen  is  each  number  ?  What  number  then  is  one-eighth 
of  sixteen  ? 

Express  :  One-eighth  of  sixteen  is  two. 

We  have  a  measure  which  holds  sixteen  quarts.  If  it  is 
an  eighth  full  how  many  quarts  are  in  the  measure  ? 

One  side  of  a  long  and  narrow  bench  is  sixteen  feet  long ; 
the  shorter  side  is  two  feet  long.  What  part  of  the  length 
is  the  width  ? 

How  many  strips  of  carpeting  two  feet  wide  will  it  take 
to  go  across  a  room  sixteen  feet  long  ?  What  part  of  the 
length  of  the  room  is  each  strip  of  carpeting? 

Fred  has  ten  watermelons  and  six  muskmelons  in  his 
little  garden.     How  many  melons  has  he  all  together  ? 

There  are  nine  buttons  on  one  of  Ned's  boots,  but  only 
seven  on  the  other  boot.     How  many  buttons  on  both  boots  ? 

Annie  is  ripping  buttons  off  of  old  dresses.  She  has 
ripped  eight  off  of  one  dress  and  eight  off  of  another  dress. 
How  many  buttons  has  she  ripped  off  all  together  ? 

There  were  sixteen  boys  with  soldier  caps.  Six  caps 
had  silver  bands  and  the  rest  had  red  bands.  How  many 
had  red  bands  ? 

At  a  summer  hotel  there  were  sixteen  rabbits  playing  on 
the  lawn.  Seven  were  white  and  the  rest  gray.  How 
many  were  gray? 


296  FIRST  STEPS   IN   NUMBER. 

If  Jack  has  sixteen  errands  to  do  and  does  eight  errands, 
how  many  more  errands  has  he  to  do?  When  he  has 
done  nine  errands,  how  many  has  he  still  to  do  ? 

James  picked  sixteen  quarts  of  cranberries.  He  put  ten 
quarts  in  one  basket,  and  the  rest  in  another  basket.  How 
many  quarts  of  cranberries  were  in  the  second  basket  ? 

If  it  costs  two  cents  to  send  an  ordinary  letter  through 
the  mail,  how  many  cents  will  it  cost  to  send  eight  letters  ? 

How  many  quarts  are  there  in  four  gallons  ? 

How  many  gills  are  there  in  four  pints  ? 

If  a  paper  of  needles  costs  eight  cents,  what  will  two 
papers  of  needles  cost  ? 

How  many  two-cent  pencils  can  I  buy  for  sixteen  cents  ? 
How  many  two-cent  stamps  ? 

When  lemons  are  four  cents  apiece,  how  many  lemons 
can  be  bought  for  sixteen  cents  ? 

When  slate  pencils  can  be  bought  for  eight  cents  a  dozen, 
how  many  dozen  can  be  bought  for  sixteen  cents  ? 

Jennie  has  sixteen  peanuts  but  she  gave  half  of  what  she 
had  to  her  sister.     How  many  did  she  give  her  sister  ? 

A  man  started  one  morning  to  ride  sixteen  miles.  When 
he  had  gone  one-fourth  of  the  distance,  he  found  the  horse 
had  lost  a  shoe  and  could  go  no  farther  on  the  rough  road, 
so  he  turned  back.     How  far  had  he  gone  ? 

A  lady  made  sixteen  turnovers  one  Thanksgiving  for 
her  eight  little  nieces.  How  many  turnovers  could  each 
have  ?  

Give  me  a  number  that  you  can  take  from  sixteen. 
(Eight.)  Sixteen  minus  eight  are  how  many  ?  I  will  ex- 
press this  on  the  board. 

16 
-8 

~8 


THE   NUMBER  SIXTEEN. 


297 


Give  another  number  that  you  can  take  from  sixteen, 
and  tell  me  the  result.  (Nine  from  sixteen  are  seven.)  I 
will  express  this  on  the  board. 

16 
-9 


You  may  express  in  the  same  way  :  Sixteen  minus  six ; 
fourteen  minus  seven ;  thirteen  minus  five ;  twelve  minus 
six ;  eleven  minus  four ;  ten  minus  six. 

Kead  what  I  express  : 


15 

12 

16 

15 

14 

11 

-10 

-10 

-6 

-5 

-10 

-10 

5 

2 

10 

10 

4 

1 

16 

15 

13 

10 

16 

15 

-7 

-6 

-10 

-10 

-8 

-7 

Complete  these  expressions : 


16^ 

2  = 

16-^ 

8  = 

^  4=  4. 

8x 

2  = 

2X 

8  = 

X  4  =  16. 

i  of  16  = 

i  of  16  = 

of  16=  4. 

16  H- 

4  = 

-;- 

8  = 

2. 

^  2=  8. 

4  X 

4  = 

X 

8  = 

16. 

X  2=16. 

1  of  16  = 

of  16  = 

8. 

of  16=  2. 

16 

15 

14 

13 

16     15 

-8 

-8 

-8 

-8 

-9    -9 

14 

13 

16 

15 

14     18 

-9 

-9 

-7 

-7 

-7    -7 

13 

16 

15 

14 

13     16 

-10 

- 

-10 

-10 

- 

-10 

-3    -6 

298  FIRST  STEPS   IN   NUMBER. 


Exercise  for  Review. 


In  two  months  from  to-day  will  be  New  Year's  day. 
"What  day  of  the  month  is  it  ?  What  month  is  it  ?  How 
many  months  have  passed  since  last  New  Year's  day? 

If  spring  and  summer  of  this  year  are  gone,  how  many 
months  remain  to  the  year?  If  one-half  of  this  year  is 
gone,  how  many  months  remain  to  the  year  ?  When  one- 
fourth  of  a  year  is  gone,  how  many  months  are  gone? 
How  many  months  remain  ? 

How  many  weeks  in  a  month  and  fourteen  days  ? 

In  twelve  quarter-dollars  how  many  dollars  ? 

In  sixteen  quarter-dollars  how  many  dollars  ? 

In  sixteen  half-dollars  how  many  dollars  ? 

If  gingham  is  sixteen  cents  a  yard,  what  will  a  half-yard 
cost?  What  will  a  quarter  of  a  yard  cost?  What  will 
one  eighth  of  a  yard  cost  ? 

Sixteen  pint  bottles  will  hold  how  many  quarts  of 
wine? 

If  James  is  fourteen  years  old,  how  many  years  ago  was 
he  one-half  as  old  as  he  is  now  ? 

I  have  a  ten-cent  piece.  What  other  two  pieces  of 
money  may  I  have  to  make  fourteen  cents  ? 

If  I  write  eight  letters  to-day  and  six  to-morrow,  how 
many  letters  shall  I  write  ? 

Mary  has  nine  figs  and  Susie  has  five  figs.  How  many 
figs  have  they  together  ? 

If  Mary  eats  one  of  her  figs  and  Susie  gets  another  fig, 
how  many  will  both  have  ? 

Fourteen  equals  how  many  twos  ? 

Fourteen  equals  how  many  sevens? 

If  this  room  is  five  yards  long,- how  many  feet  long  is  the 
room? 


THE   NUMBER  SIXTEEN.  299 

A  stick  that  is  fifteen  feet  long  can  be  cut  into  how  many 
yard-sticks  ? 

When  John  measured  the  platform  he  found  it  would 
contain  his  foot-rule  fifteen  times.  How  many  yards  long 
is  the  platform  ? 

Fifteen  is  how  many  threes? 

If  you  are  in  school  five  hours  a  day,  how  many  hours 
are  you  in  school  three  days  ? 

Nellie  drew  a  triangle  which  was  five  inches  on  each 
side.     How  far  was  it  round  the  triangle  ? 

I  saw  a  garden  plot  in  the  shape  of  a  triangle  that  was 
five  feet  on  a  side.     How  far  was  it  round  the  plot  ? 

If  plants  were  set  around  the  outside  a  foot  apart,  how 
many  plants  were  set  around  the  bed  ?  Draw  the  plot  and 
see  if  you  are  right. 

A  gardener  had  six  Scotch  roses  and  half  as  many  more 
English  roses.     How  many  roses  had  he  in  all  ? 

If  it  takes  six  yards  of  dress  goods  to  make  Fanny  a 
dress,  and  half  as  many  more  yards  to  make  her  mother  a 
dress,  how  many  yards  are  required  for  both  dresses  ? 

How  many  strokes  will  the  clock  give  in  striking  seven 
and  eight? 

Harry  went  to  visit  his  cousin  for  a  week  but  stayed 
eight  days  more  than  a  week.  How  many  days  did  he 
stay  all  together  ? 

A  round  block  is  fifteen  inches  round  and  one-third  as 
many  inches  across.    How  many  inches  across  is  the  block  ? 

My  paper-weight  is  fifteen  inches  round  and  one-third 
as  many  inches  across.  How  many  inches  across  is  the 
weight  ? 

This  stick  is  a  foot  and  three  inches  in  length.  How 
many  inches  long  is  the  stick  ? 

Annie  is  five  years  old  and  her  brother  twice  as  old. 
What  is  the  sum  of  their  ages  ? 


300  FIRST  STEPS   IN   NUMBER. 

Henry  is  fifteen  years  old  and  his  brother  five  years  old. 
"What  is  the  difference  of  their  ages  ? 

A  cask  has  fifteen  gallons  of  apple  sauce  in .  it.  After 
seven  gallons  are  dipped  out  how  many  gallons  will 
remain  in  the  cask  ? 

Count  by  threes  to  fifteen. 

Count  by  fives  to  fifteen. 

What  three  equal  numbers  make  fifteen  ? 

What  five  equal  numbers  make  fifteen  ? 

Harry  had  six  words  written  on  one  side  of  his  slate,  and 
one  more  than  six  words  written  on  the  other  side  of  his 
slate.     How  many  words  had  he  wi*itten  in  all  ? 

Thirteen  is  how  many  more  than  a  dozen  ? 

I  have  a  ten-cent  piece.  Tell  me  what  other  piece  of 
money  I  must  have  to  make  thirteen  cents. 

If  I  pick  six  quarts  and  a  half  of  raspberries  how  many 
pints  do  I  pick  ? 

A  man  bought  eight  pounds  of  brown  sugar  and  five 
pounds  of  white  sugar.  How  many  pounds  of  sugar  did 
he  buy? 

There  are  eight  cows  and  five  calves  in  a  pasture.  How 
many  cattle  are  in  the  pasture  ? 

Make  up  an  example  for  what  I  express  on  the  board : 


8  +  5 

9  +  4 

X    7  =  14. 

9  +  3 

9  +  5 

X    3  =  15. 

10  +  4 

9  +  6 

X    4  =  16. 

7  +  5 

9  +  7 

+  10  =  16. 

6  +  5 

6  +  7 

+    7  =  12. 

3 

1 

4 

2 

4 

2 

5 

5 

6 

7 

3 

4 

3 

5 

4 

3 

THE   NUMBER  SIXTEEN.  301 


16 

15 

14 

13 

-6 

-5 

-10 

-10 

15 

15 

16 

16 

-7 

-13 

-14 

-12 

Express  on  the  board : 

One-half  of  two.  One-third  of  fifteen. 

One-half  of  six.  One-third  of  twelve. 

One-half  of  ten.  One-third  of  six. 

One-half  of  fourteen.  One-fourth  of  four. 

One-half  of  sixteen.  One-fourth  of  twelve. 

One-half  of  twelve.  One-fourth  of  eight. 

One-half  of  eight.  One-fourth  of  sixteen. 

One-half  of  four.  One-eighth  of  sixteen. 

One-third  of  three.  One-eighth  of  eight. 

One-third  of  nine.  One-half  of  one. 

Fill  out : 

8  +  4  =  +  8  =  16. 

9  +  3  =  -f  8  =  14. 
10  +  2  -                                 -f  8  =  12. 

.  11  +  1  =  +8-10. 

7  +  5=  -8=    8. 

6  +  6=  -8==    6. 

7  +  6-  -8=    4. 

8  +  5--=  -8=    2. 


CHAPTEE   XVII. 

THE   NUMBER  SEVENTEEN. 


§  39.    The  Number  Seventeen. 

Take  a  bundle  of  ten  splints.  Take  seven  more  splints. 
Who  knows  how  many  ten  and  seven  are  ? 

Express  on  the  board :  Ten  and  seven  are  seventeen. 

Give  an  example  for  ten  and  seven. 

Seventeen  minus  seven  are  how  many  ? 

Seventeen  minus  ten  are  how  many  ? 

Express  on  the  board  all  the  facts  in  seventeen  that  you 
know. 

If  there  were  ten  geranium  blossoms  on  a  plant  yesterday, 
and  now  there  are  seven  more  blossoms,  how  many  blossoms 
are  on  my  plant  ? 

If  one  of  yesterday's  blossoms  drop  off,  how  many  old 
blossoms  will  remain?  If  one  more  new  blossom  comes, 
how  many  new  blossoms  will  there  be?  If  one  blossom 
dies  and  one  new  blossom  comes,  are  there  as  many  now  as 
before  ?     Nine  and  eight  are  how  many  then  ? 

Three  three-cent  pieces  and  four  two-cent  pieces  of  money 
are  how  much  money  ? 

Name  two  numbers  one  of  which  is  one  more  than  the 
other  that  together  make  seventeen. 

Amy  is  seventeen  years  old.  How  old  was  she  seven 
years  ago  ?  How  old  was  she  ten  years  ago  ?  nine  years 
ago  ?  eight  years  ago  ? 


THE  NUMBER  SEVENTEEN.  303 

Ned's  language-book  and  writing-book  together  cost 
seventeen  cents.  If  his  language-book  cost  nine  cents, 
what  did  his  writing-book  cost  ? 

If  a  man's  coat  cost  seventeen  dollars,  and  a  boy's  jacket 
cost  eight  dollars,  how  much  more  did  the  coat  cost  than 
the  jacket  ? 

Two  five-cent  pieces  of  money,  two  three-cent  pieces,  and 
one  cent  are  how  much  money  ? 

Fill  out  the  blanks : 


10+7  = 

17 

17 

17-10  = 

-10 

-9 

9+    8  = 

17-7  = 

17 

17 

17-    9  = 

-8 

-7 

17-8  = 

17  X    1  = 

17 

17 

17^    1  = 

-5 
One-Sixth. 

-6 

Into  how  many  pieces  have  I  divided  this  circle  ?  (Six 
pieces.)  Into  what  kind  of  pieces?  (Equal.)  Into  what 
then  have  I  divided  this  circle  ? 

Into  what  have  I  divided  this  ring  ?     (Six  equal  pieces.) 

Into  what  have  I  divided  this  apple  ?  this  leaf  of  paper  ? 

Into  how  many  equal  parts  have  I  divided  this  line? 

Each  part  of  the  line  is  one-sixth  of  the  whole  line.  Show 
me  one-sixth  of  the  line. 

Each  one  of  the  six  equal  parts  of  the  apple  is  one-sixth 
of  the  apple.     Show  me  one-sixth  of  the  apple. 

Show  me  one-sixth  of  the  ring  I  divided. 

How  many  such  parts  will  it  take  to  make  the  ring  ? 

Show  me  one-sixth  of  the  circle  I  divided. 


304  FIRST  STEPS   IN   NUMBER. 

How  many  such  parts  will  it  take  to  make  the  circle  ? 

Draw  a  triangle.  Divide  the  base  into  halves,  and  divide 
each  half  into  thirds.  Into  how  many  equal  parts  is  the 
base  divided  ?  ,  What  part  of  the  whole  base  is  each  of  the 
parts  into  which  it  is  divided?  Write  *'s"  under  each 
sixth.     How  many  times  have  you  written  *'  s  "  ? 

Connect  the  vertex  with  each  point  of  division  in  the  base. 
How  many  triangles  have  you  made  ?  What  part  of  the 
large  triangle  is  each  small  triangle  ? 

See  if  you  can  divide  a  circle  into  sixths.  This  rectangle 
into  sixths. 

Show  me  what  you  think  to  be  a  sixth  of  the  edge  of  this 
table  ;  of  the  other  edge  of  the  table. 

What  part  of  this  pencil  is  one-sixth  of  the  whole 
pencil  ? 

Call  these  six  blocks  a  pie.   Divide  this         g     g     B 
pie  into  six  equal  pieces.     What  part  of 
the  whole  pie  is  each  piece?  M     &     & 

Call  these  six  blocks  an  orange  that 
is  split  open  on  one  side  so  that  it  lies  nearly  flat.     Divide 
the  orange  into  sixths. 

Take  twelve  blocks.  Divide  the  number  into  six  equal 
groups.  What  part  of  twelve  is  each  group  ?  How  many 
in  each  group  ? 

What  number  then  is  one-sixth  of  twelve  ?  How  many 
such  numbers  will  it  take  to  make  twelve  ? 

If  you  eat  one-sixth  of  a  dozen  eggs,  how  many  eggs  will 
you  eat? 

Into  how  many  sixths  can  you  cut  a  pie  ?  into  how  many 
fourths  ?  into  how  many  thirds  ?  into  how  many  halves  ? 

Which  is  larger,  a  half  or  a  sixth  of  the  same  pie?  a  half 
or  a  fourth  of  the  same  pie  ? 

Express :  One-sixth  of  twelve  is  two.  One-sixth  of  six 
is  one. 


CHAPTER  XVIII. 

THE  NUMBER  EIGHTEEN. 


§  40.   The  Number  Eighteen. 

Who  knows  how  many  ten  and  eight  are  ?  Find  out  with 
the  splints  if  you  do  not  know. 

Express  the  fact  on  the  board. 

Give  an  example  for  the  fact. 

If  you  take  one  from  the  ten  and  put  it  with  eight,  what 
two  equal  numbers  will  you  have  ?  What  is  the  sum  of 
nine  and  nine  ? 

Give  examples  for  nine  and  nine. 

Since  nine  and  nine  make  eighteen,  how  many  nines 
make  eighteen  ? 

Express  :  Two  nines  are  eighteen. 

If  each  ball  club  has  nine  boys,  how  many  boys  will  it 
take  for  two  ball  clubs  ? 

If  there  are  nine  rings  on  one  curtain  rod,  how  many  are 
there  on  two  curtain  rods  ? 

If  two  nines  make  eighteen,  how  many  nines  will  you 
find  in  eighteen? 

Express :  Eighteen  divided  by  nine  are  two. 

I  ironed  eighteen  handkerchiefs,  and  laid  them  in  piles 
with  nine  in  each  pile.     How  many  piles  did  I  make  ? 

When  calico  is  nine  cents  a  yard,  how  many  yards  can 
be  bought  for  eighteen  cents  ? 

Into  what  two  equal  numbers  may  eighteen  be  divided  ? 


306  '  FIRST   STEPS   IN   NUMBER. 

What  part  of  eighteen  is  each  number  ?  What  then  is  one- 
half  of  eighteen  ? 

We  had  eighteen  young  turkeys,  but  half  of  them  strayed 
away  in  the  ^\^et  grass  and  died.     How  many  had  we  then  ? 

John  picked  eighteen  quarts  of  cranberries,  and  Harry 
picked  half  as  many  quarts.  How  many  quarts  of  cran- 
berries did  Harry  pick  ? 

Who  knows  how  many  sixes  there  are  in  eighteen  ?  Find 
out  with  the  splints  if  you  are  not  sure. 

Express  this  fact  on  the  board. 

If  there  are  eighteen  pencils  in  a  box,  done  up  in  bundles 
of  six  each,  how  many  bundles  are  there  in  the  box? 

If  there  are  eighteen  pear  trees  in  an  orchard,  arranged 
in  rows  of  six  each,  how  many  rows  of  pear  trees  are  there  ? 

A  man  who  is  packing  eggs  in  a  box  puts  a  half  dozen 
eggs  in  each  layer.  How  many  layers  will  eighteen  eggs 
make? 

Give  me  an  example  for  eighteen  divided  by  six. 

If  you  find  three  sixes  in  eighteen,  how  many  sixes  must 
you  take  to  make  eighteen  ? 

Express  :  Three  sixes  are  eighteen. 

If  you  buy  a  half  dozen  oranges  to-day,  to-morrow,  and 
the  next  day,  how  many  oranges  will  you  buy  in  all  ? 

If  there  are  half  a  dozen  pies  on  each  shelf,  how  many 
pies  are  on  three  shelves  ?  How  many  pies  are  there  on 
two  shelves?     What  part  of  a  dozen  on  the  next  shelf? 

How  many  did  you  say  there  were  on  the  three  shelves  ? 
Then  one  dozen  and  a  half  are  how  many  ? 

A  dozen  and  a  half  apples  are  how  many  apples  ?  A 
dozen  and  a  half  eggs  are  how  many  eggs  ? 

What  three  equal  numbers  make  eighteen  ? 

What  part  of  eighteen  is  each  of  the  three  equal  numbers 
which  make  eighteen  ? 

What  part  of  eighteen  is  six  ? 


THE   NUMBER   EIGHTEEN.  307 

Express  on  the  board  :  One-third  of  eighteen  is  six. 

Give  an  example  for  this  fact. 

Express  on  the  board :  Six  and  six  and  six  are  eighteen. 

"What  two  equal  numbers  make  six  ? 

Write  ''  three  and  three  "  under  each  six. 

Eead  six  and  six  and  six  are  eighteen,  in  threes. 

Sow  many  threes  are  eighteen  ? 

Express  :  Six  threes  are  eighteen. 

Give  an  example  for  this  fact. 

If  you  have  six  three-cent  pieces,  how  much  money  have 
you? 

If  you  buy  a  half  dozen  three-cent  lead  pencils,  how  much 
money  will  you  pay  ? 

Six  triangles  have  how  many  sides?  have  how  many 
corners  ? 

If  you  put  a  dot  in  each  corner  of  six  triangles,  how  many 
dots  will  you  make  ? 

If  it  takes  six  threes  to  make  eighteen,  how  many  threes 
can  you  find  in  eighteen  ? 

Express  this  fact  on  the  board. 

Eighteen  cents  will  buy  how  many  three-cent  pencils? 
how  many  three-cent  books  ?  how  many  peaches  at  three 
cents  each  ? 

Give  an  example  for  eighteen  divided  by  three. 

What  six  equal  numbers  make  eighteen  ? 

What  part  of  eighteen  is  each  of  these  numbers  ?  What 
part  then  of  eighteen  is  three  ? 

Express  :  One-sixth  of  eighteen  is  three. 

If  I  distribute  eighteen  pencils  equally  among  six  chil- 
dren, how  many  pencils  do  I  give  each  child? 

A  lady  cut  a  cake  into  eighteen  equal  pieces.  If  a 
sixth  of  the  cake  was  eaten,  how  many  pieces  were 
eaten  ? 

If  a  large  watermelon  was  cut  into  eighteen  pieces,  and  I 


308  FIRST  STEPS   IN   NUMBER. 

put  a  sixth  of  the  number  of  pieces  on  a  separate  plate,  how 
many  pieces  did  I  put  on  the  plate  ? 

Give  an  example  for  one-sixth  of  eighteen. 

Who  can  tell  how  many  twos  in  eighteen  ?  Find  out 
with  the  splints  if  you  do  not  know. 

Express  the  fact  on  the  board. 

How  many  two-cent  stamps  can  I  buy  for  eighteen  cents  ? 

How  many  pairs  of  gloves  are  there  in  eighteen  gloves  ? 

How  many  quarts  are  there  in  eighteen  pints  ? 

Eighteen  shafts  will  supply  how  many  wagons  ? 

If  there  are  nine  twos  in  eighteen,  how  many  two-cent 
pieces  will  it  take  to  equal  eighteen  cents? 

How  many  knobs  are  required  for  nine  doors  ? 

How  many  eyes  have  nine  boys  ? 

Nine  oysters  have  how  many  shells  ? 

Nine  sheets  of  paper  have  how  many  leaves  ? 

Who  has  an  example  for  nine  twos  are  eighteen  ? 

Express  on  the  board  all  the  facts  in  eighteen.  Who  has 
eighteen  facts  expressed  ? 

Illustrate  with  drawings  half  of  the  facts  you  have 
expressed. 

Tell  me  about  your  drawings. 

Illustrate  the  examples  I  give  you. 

One  man  rowed  down  the  river  nine  miles,  and  another 
man  starting  at  the  same  place  rowed  up  the  river  nine 
miles. 

There  were  three  rows  of  pies  in  the  pantry,  six  in  each 
row. 

There  were  enough  quart-bottles  on  a  shelf  to  hold  eigh- 
teen pints. 

There  were  enough  three-quart  pickle  jars  to  hold  eighteen 
quarts  of  pickles. 

There  were  enough  pans  in  the  dairy  to  hold  eighteen 
quarts  of  milk  if  six  quarts  were  put  in  each  pan. 


THE   NUMBER  EIGHTEEN.  309 

Express  the  examples  I  give  you,  and  also  the  answer. 
(The  pupil  understands  by  this  direction  that  he  is  to 
express  the  operation  which  the  conditions  of  each  problem 
require,  and  the  result  of  the  operation.) 

There  were  ten  English  sparrows  drinking  out  of  the 
basin  of  a  fountain,  and  eight  more  on  the  ground  around 
the  fountain.  How  many  sparrows  were  there  in  all? 
(10  +  8  =  18.) 

If  one  base-ball  nine  plays  against  another  base-ball  nine, 
how  many  boys  are  playing  ?     (9  +  9  —  18.) 

I  bought  three  quarts  of  hulled  corn  at  six  cents  a  quart. 
What  did  I  pay  ?     (3x6  =  18.) 

I  bought  six  hat  pins  at  three  cents  apiece.  What  did  I 
pay?     (6x3 --18.) 

I  had  eighteen  curtain  rings,  and  it  took  two  rings  for 
each  curtain  loop.  How  many  loops  could  I  supply  with 
rings?     (18 -^2  =-9.) 

There  were  eighteen  feet  in  a  chain.  How  many  yards 
were  there  in  the  chain  ?     (18  -f-  3  =  6.) 

If  it  takes  six  strips  of  carpeting,  each  strip  a  yard  wide, 
to  go  across  my  room,  how  many  feet  long  is  my  room  ? 
(6  X  3  -  18.) 

This  morning  the  cook  had  a  dozen  and  a  half  eggs.  She 
used  a  third  of  them  in  making  a  pudding  for  dinner.  How 
many  eggs  did  she  use  ?     (^  of  18  =  6.) 

A  boy  who  had  eighteen  rabbits  sold  half  of  them.  How 
many  rabbits  did  he  sell  ?     (|-  of  18  =  9.) 

It  took  eighteen  yards  of  ribbon  to  trim  six  hats.  How 
many  yards  of  ribbon  were  used  for  each  hat  ?  (^  of  18  =  3.) 

I  distributed  eighteen  nuts  equally  between  two  boys. 
How  many  nuts  did  I  give  to  each  boy  ?     (i  of  18  ===  9.) 

Three  boys  together  earned  eighteen  cents,  and  all  received 
an  equal  amount  of  money.  How  much  did  each  receive? 
(1  of  18  =  6.) 


310 


FIRST  STEPS   IN  NUMBER. 


Supply  the  missing  term  in  these  expressions : 


18-2: 

18-3^ 
18 -t-    6^ 

18 -V-     9: 

I  of  18  : 
-1-  of  18  : 
1-  of   18  : 

9x    2  = 

6x 

2x 

3x 
10  + 

9  + 
18- 
18 
18-8: 

8+10: 
18  ^   18  : 

9+  9: 
18-  6: 
18  -  18  : 
12+       6: 


3: 

9: 
6: 
8: 
9 
10 
9 


18 


18 
-13 


18- 
18- 
18- 
18- 

9  + 

10  + 
8  + 

12  + 
9x 
2x 
6x 
3x 

18 

18 -f- 

18^ 

18 

18 
iof 
I  of 
iof 
6  + 

18  X 

18 
14 


10 
8, 
9 

12 

18, 

18, 

18, 

18, 

18, 

18, 

18. 

18, 

9 

6 

3 

2, 

18 

9 

6, 

3 

18, 
18, 

18 
-5 


18 

18 

18 

18 

-10 

-11 

-17 

-2 

18 

18 

18 

18 

-12 

-7 

-16 

-4 

18 

18 

18 

18 

-6 

-9 

-15 

-3 

CHAPTEE  XIX. 

THE   NUMBER  NINETEEN. 


§  41.     The  Number  Nineteen. 

Show  me  a  bundle  of  ten  splints,  and  nine  single  splints. 
Who  knows  what  number  he  has  shown  me  ? 

Express  the  number  on  the  board. 

A  ten-cent  piece  and  three  three-cent  pieces  of  money 
will  make  hi)w  much  money  ? 

Two  five-cent  pieces  of  money  and  three  three-cent  pieces 
of  money  will  make  how  much  money  ? 

Give  examples  for  ten  and  nine. 

Express  just  the  sum  of  ten  and  nine  on  the  board.    (19.) 

Express  underneath  it  the  sum  of  ten  and  eight. 

Express  the  sum  of  ten  and  seven  ;  of  ten  and  six  ;  of  ten 
and  five ;  of  ten  and  four ;  of  ten  and  three ;  of  ten  and 
two  ;  of  ten  and  one  ;  of  ten  and  none. 

How  many  tens  has  each  one  of  these  numbers  ? 

"Which  number  has  the  most  ones  besides  the  one  ten? 
Which  number  has  eight  ones  beside  the  one  ten  ?  Which 
number  has  seven  ones  besides  the  one  ten  ? 

Show  me  the  column  of  tens  ;  the  column  of  ones. 

What  is  the  difference  between  none  and  nine  ?  between 
ten  and  nineteen  ?  between  one  and  nine  ?  between  eleven 
and  nineteen?  between  four  and  nine?  between  fourteen 
and  nineteen  ?  between  ^ve  and  eight  ?  between  fifteen  and 
eighteen  ?  between  fourteen  and  eighteen  ?  between  fifteen 
and  nineteen  ?  between  thirteen  and  sixteen  ?  between 
twelve  and  nineteen  ? 


312  FIRST   STEPS   IN   NUMBER. 

Express :  Two  eights  are  sixteen. 

Three  fives  are  fifteen. 
Four  threes  are  twelve. 
Five  threes  are  fifteen. 
Six  threes  are  eighteen. 
I  will  express  what  you  have  written  in  this  way : 
8  5  3  3  3 

2  3  4  5  6 

16  15  12  15  18 

Express  in  this  new  way  : 

Three  fours  are  twelve. 
Two  nines  are  eighteen. 
Four  fours  are  sixteen. 
Three  sixes  are  eighteen. 
Nine  twos  are  eighteen. 
Two  sixes  are  twelve. 

Exercise  for  Revie>v. 

How  many  strokes  will  a  clock  give  in  striking  five  and 
six  ?  in  striking  six  and  seven  ?   in  striking  seven  and  eight  ? 

How  many  strokes  will  a  clock  give  between  half-past 
three  and  half-past  six  ? 

If  the  face  of  a  clock  is  a  foot  round,  how  many  inches 
does  the  point  of  the  long  hand  move  over  in  going  from 
twelve  to  six  ?  in  going  from  twelve  to  twelve  ?  in  going 
once  and  a  half  round  the  clock  ? 

How  long  a  time  will  it  take  the  long  hand  to  move  over 
eighteen  inches  ?  How  long  will  it  take  the  short  hand  to 
move  over  eighteen  inches? 

If  that  blackboard  is  eighteen  feet  in  length,  how^  many 
yards  long  is  the  blackboard  ? 

If  this  table  is  six  feet  on  one  side,  and  three  feet  on  the 
other  side,  how  many  yards  is  it  all  round  the  table  ? 


THE   NUMBER   NINETEEN.  ,  313 

This  stick  is  a  foot  and  a  half  long.  How  many  inches 
in  length  is  the  stick  ? 

The  distance  from  the  floor  to  the  first  round  of  a  chair 
is  half  a  foot ;  from  the  first  round  to  the  next  round  is  half 
a  foot,  and  from  the  second  round  to  the  seat  of  the  chair 
half  a  foot.  How  many  inches  high  is  the  seat  of  the 
chair  ? 

If  wood  is  sawed  into  sticks  a  foot  and  a  half  long,  how 
long  must  the  wood  be  to  make  two  sticks  ?  What  part 
of  a  yard  ? 

If  a  shed  is  eighteen  feet  from  the  roof  to  the  ground, 
how  many  yards  is  the  roof  from  the  ground? 

A  yoke  of  oxen  will  require  how  many  shoes  ? 

Four  horses  will  require  how  many  shoes  ? 

Sixteen  quarts  of  molasses  will  fill  how  many  gallon  jugs? 

Eighteen  half-pint  jelly  glasses  will  hold  how  many  pints 
of  jelly?  how  many  quarts  of  jelly?  How  many  more 
glasses  will  it  take  to  hold  five  quarts  of  jelly? 

A  week  and  ten  more  days  are  how  many  days  ? 

I  bought  two  bottles  of  ink.  For  one  bottle  I  paid  nine 
cents,  and  for  the  other  bottle  one  cent  less.  How  much 
did  I  pay  for  both  bottles  of  ink  ? 

Eighteen  equals  how  many  twos?  how  many  threes? 
how  many  sixes  ?  how  many  nines  ? 

What  is  one  of  the  nine  equal  numbers  that  make  eigh- 
teen ?  one  of  the  six  equal  numbers  ?  one  of  the  three  equal 
numbers?  one  of  the  two  equal  numbers? 

Sixteen  equals  how  many  twos  ?  how  many  fours  ?  how 
many  eights? 

Fifteen  equals  how  many  threes  ?  how  many  fives  ? 

Fourteen  equals  how  many  twos  ?  how  many  sevens  ? 

Twelve  equals  how  many  twos?  how  many  threes?  how 
many  fours  ?  how  many  sixes  ? 


CHAPTER  XX. 

TENS. 


§  42.     Tens. 

Take  two  tens.     Who  knows  how  many  two  tens  are  ? 

Take  three  tens.     How  many  are  three  tens  ? 

Take  four  tens.     How  many  are  four  tens  ? 

Show  me  fifty.     How  many  tens  make  fifty  ? 

Show  me  sixty.     How  many  tens  make  sixty  ? 

Kead  the  number  I  show  you.  (Seventy.  Forty. 
Eighty.     Thirty.     Ninety.) 

In  thirty,  how  many  tens?  In  fifty,  how  many  tens? 
In  sixty,  how  many  tens? 

Nine  tens  are  how  many?  Eight  tens  are  how  many? 
Four  tens  are  how  many  ?     Six  tens  are  how  many  ? 

Show  me  with  bundles  of  tens  the  answers  to  the  ques- 
tions I  ask  you : 

I  have  two  ten-cent  pieces  in  my  hand.  How  much 
money  have  I  ? 

Jennie  bought  four  yards  of  calico  at  ten  cents  a  yard. 
How  much  did  she  pay  for  the  calico  ? 

James  bought  ^Ye  pounds  of  sugar  at  ten  cents  a  pound. 
How  much  did  he  pay  for  the  sugar  ? 

There  are  eight  rows  of  trees  in  an  orchard,  and  ten 
trees  in  each  row.     How  many  trees  are  in  the  orchard  ? 

If  a  baker  sells  a  loaf  of  bread  for  ten  cents,  how  much 
will  he  receive  for  nine  loaves  of  bread  ? 


TENS.  315 

Express  the  number  ten  on  the  board. 

Who  can  express  two  tens  or  twenty?  three  tens  or 
thirty  ?  four  tens  or  forty  ? 

Express  fifty  ;  sixty ;  seventy  ;  eighty  ;  ninety  ;  ten  tens 
or  one  hundred. 

Point  to  a  number  that  has  just  two  tens  in  it ;  that  has 
three  tens  in  it ;  that  has  six  tens  in  it ;  that  has  five  tens 
in  it ;  that  has  seven  tens  in  it ;  that  has  eight  tens  in  it. 

Point  to  the  column  of  tens.  Which  number  has  the 
least  number  of  tens  ?  which  number  has  the  greatest  num- 
ber of  tens  ? 

Express  on  the  board  the  sum  of  ten  and  ten. 

How  many  fingers  and  toes  have  you,  counted  together? 

If  it  is  ten  miles  from  here  to  Boston,  how  far  is  it  to 
Boston  and  back  ? 

Express  on  the  board  the  sum  of  twenty  and  ten. 

A  twenty-dollar  bill  and  a  ten-dollar  bill  are  how  much 
money  ? 

If  we  own  twenty  hens  and  ten  ducks,  how  many  fowls 
do  we  own  ? 

If  I  am  twenty  years  old,  and  you  are  ten  years  old, 
what  is  the  sum  of  our  ages  ? 

Express  the  sum  of  thirty  and  ten. 

If  you  have  thirty  cents,  and  I  give  you  a  ten-cent  piece, 
how  much  money  will  you  have  ? 

If  you  read  thirty  minutes,  and  write  ten  minutes,  how 
long  a  time  is  required  for  reading  and  writing  ? 

Express  the  sum  of  forty  and  ten. 

If  a  barrel  holds  forty  gallons  of  vinegar,  and  a  cask 
holds  ten  gallons,  how  much  will  both  hold  together  ? 

A  train  ran  forty  miles  the  first  hour,  but,  owing  to  a 
break  in  the  engine,  it  ran  but  ten  miles  the  next  hour. 
How  far  did  the  train  run  in  the  two  hours  ? 

A  small  broom  cost  forty  cents,  and  a  dust-pan  ten  cents. 


316  FIRST  STEPS   IN  NUMBER. 

How  much  did  both  cost  ?  What  part  of  a  dollar  is  fifty 
cents  ? 

If  I  have  half  a  dollar,  and  you  have  ten  cents,  how  much 
money  have  we  together  ? 

If  I  buy  a  half-dollar's  worth  of  postage  stamps,  and  ten 
postal  cards  at  a  cent  each,  how  much  money  do  I  spend 
for  both? 

Express  the  sum  of  fifty  and  ten. 

Express  the  sum  of  sixty  and  ten. 

If  you  have  sixty  cents  in  your  bank,  and  your  father 
puts  in  two  five-cent  pieces,  how  much  money  will  there  be 
in  your  bank  ? 

If  a  gallon  of  molasses  costs  sixty  cents,  and  a  pound  of 
sugar  costs  ten  cents,  how  much  do  both  cost  ? 

Express  the  sum  of  seventy  and  ten. 

I  bought  a  half-bushel  of  peaches  for  seventy  cents,  and 
a  half-dozen  pears  for  ten  cents.  How  much  did  I  pay  for 
both? 

My  winter  cloak  cost  seventy  dollars,  and  my  hat  ten 
dollars.     How  much  did  both  together  cost? 

Express  the  sum  of  eighty  and  ten. 

A  man  had  ten  hens  and  eighty  chickens.  How  many 
hens  and  chickens  had  he  together? 

A  man  bought  a  chamber-set  for  eighty  dollars,  and  a 
lamp  for  ten  dollars.     How  much  did  he  pay  for  both  ? 

Express  the  sum  of  ninety  and  ten. 

If  you  have  nine  ten-cent  pieces,  and  I  give  you  another 
ten-cent  piece,  how  much  money  will  you  have  ? 

If  there  were  ninety  cans  on  one  shelf,  and  ten  on  an- 
other shelf,  how  many  cans  were  on  both  shelves  together  ? 

If  I  buy  ninety  pounds  of  fine  flour,  and  ten  pounds  of 
Graham  flour,  how  many  pounds  of  flour  shall  I  buy  ? 

We  own  a  clock  that  is  ninety  years  old.  How  old  will 
it  be  in  ten  years  from  this  time  ? 


TENS.  317 

I  have  a  piece  of  money  that  was  coined  ninety  years 
ago.     How  old  will  it  be  ten  years  from  now  ? 

Express  twenty  on  the  board.  Express  thirty  below  it. 
Two  tens  and  three  tens  are  how  many  tens  ?  Draw  a  line, 
and  express  the  answer.  Find  the  sum  of  thirty  and  forty 
by  adding  the  tens.  Find  the  sum  of  fifty  and  forty  in  the 
same  way.  Find  the  sum  of  fifty  and  twenty  ;  of  sixty  and 
thirty ;  of  forty  and  forty ;  of  fifty  and  fifty ;  of  seventy 
and  twenty ;  of  sixty  and  twenty ;  of  twenty  and  thirty  ; 
of  thirty  and  thirty ;  of  thirty  and  fifty ;  of  twenty  and 
forty ;  of  twenty  and  twenty. 

There  are  twenty  quires  of  paper  in  a  ream.  How  many 
quires  of  paper  are  there  in  two  reams?  in  three  reams? 
in  four  reams  ?  in  five  reams  ? 

Twenty  years  is  called  a  score  of  years.  How  old  is  a 
man  who  is  two  score  years  ?  How  old  is  a  man  who  is 
four  score  years  ? 

How  many  pennies  have  I  if  I  have  half  a  score  of  pen- 
nies ?  How  many  errands  has  a  boy  to  do  if  he  has  half  a 
score  of  errands  to  do  ? 

How  many  children  were  playing  in  the  school-yard  if 
there  were  three  score  of  children  ? 

How  many  weeks  are  there  in  two  terms  of  twenty  weeks 
each? 

Five  twenty-dollar  gold  pieces  are  how  much  money  ? 

20 
Express  two  times  twenty  thus  : 

A 

Express  in  a  similar  way  :  Three  times  twenty ;  four  times 
twenty ;  five  times  twenty ;  twenty  times  two ;  twenty 
times  three ;  twenty  times  four ;  twenty  times  five. 

How  many  days  are  there  in  two  months  of  thirty  days 
each? 

How  many  yards  of  carpeting  will  be  required  for  three 
rooms,  if  each  room  takes  thirty  yards  ? 


318  FIRST  STEPS   IN   NUMBER. 

If  a  man  who  is  now  forty  years  old  lives  to  be  twice  as 
old  as  lie  is  now,  how  old  will  he  be  ? 

If  I  teach  school  forty  weeks  a  year,  how  many  weeks 
shall  I  teach  in  two  years? 

If  you  owe  me  two  half-dollars,  how  many  cents  do  you 
owe  me  ? 

If  cloth  is  fifty  cents  a  yard,  how  much  will  two  yards 
cost? 

What  will  two  boxes  of  paper  cost  at  fifty  cents  a  box  ? 

Express  :  Two  times  thirty  ;  three  times  thirty ;  two 
times  forty ;  two  times  fifty ;  thirty  times  two  ;  thirty  times 
three  ;  forty  times  two ;  fifty  times  two. 


Take  this  number  work  : 

20  + 10  = 

60+10  = 

3x10  = 

7x10  = 

30+10  = 

70  + 10  = 

2x10  = 

6x10  = 

40  + 10  = 

80+10  = 

5x10  = 

9x10  = 

50  +  10  = 

90+10  = 

4x10  = 

8x10  = 

30 

50 

40 

60 

+  40 

+  20 

+  40 

+  20 

30 

20 

50 

60 

+  30 

+  40 

+  40 

+  30 

50 

20 

30 

70 

+  50 

+  30 

+  50 

+  20 

20            20 

20            20 

30 

30            40 

2              3 

4              5 

2 

3              2 

TENS.  319 

I  am  twenty  years  old.     How  old  was  I  ten  years  ago  ? 

It  is  now  the  thirtieth  of  the  month.  What  day  of  the 
month  was  it  ten  days  ago  ? 

A  small  peach-tree  bore  fifty  peaches.  Ten  peaches 
dropped  off  before  they  were  ripe.  How  many  peaches 
stayed  on  the  tree  to  ripen? 

A  man  had  seventy  silk  circulars  in  the  morning,  but 
sold  ten  during  the  day.     How  many  had  he  left  ? 

A  ninety-cent  book  was  sold  to  me  for  ten  cents  under 
price.     How  much  did  I  pay  for  the  book  ? 

I  gave  a  dollar  bill  in  payment  for  some  work  done  at 
the  jeweller's,  and  received  ten  cents  in  change.  How  much 
did  I  pay  for  the  work  ? 

In  a  flight  of  stairs  there  are  forty  steps.  There  are  ten 
steps  from  the  floor  to  the  first  landing.  How  many  steps 
from  the  first  landing  to  the  top  ? 

I  was  away  for  a  visit  of  sixty  days.  If  I  spent  ten  days 
in  going  and  returning,  how  many  days  had  I  for  my  visit  ? 

A  church  in  our  town  was  built  eighty  years  ago.  A 
large  white  house  that  stands  near  it  was  built  ten  years 
afterwards.     How  many  years  has  the  house  been  built  ? 

Express  fifty  on  the  board.  Express  beneath  it  thirty. 
Five  tens  minus  three  tens  are  how  many  tens?  Draw  a 
line  and  express  the  answer.  Find  the  diflerence  between 
fifty  and  twenty  by  subtracting  the  tens.  Find  the  difler- 
ence between  fifty  and  forty ;  between  fifty  and  ten ;  be- 
tween seventy  and  thirty ;  between  seventy  and  twenty ; 
between  seventy  and  fifty ;  between  seventy  and  forty ; 
between  seventy  and  sixty ;  between  seventy  and  ten ; 
between  sixty  and  twenty ;  between  sixty  and  forty ;  be- 
tween sixty  and  ten  ;  between  sixty  and  thirty ;  between 
sixty  and  fifty ;  between  forty  and  ten  ;  between  forty  and 
thirty ;  between  forty  and  twenty ;  between  eighty  and 
thirty;    between  eighty   and   forty;   between   eighty   and 


320 


FIRST  STEPS  IN  NITMBEH. 


ten  ;  between  eighty  and  twenty  ;  between  eighty  and  fifty 
between  eighty  and  seventy ;  between  ninety  and  thirty 
between  ninety  and  sixty ;  between  ninety  and  twenty 
between  ninety  and  seventy. 

How  many  quarts  of  berries,  at  ten  cents  a  quart,  can  be 
bought  for  thirty  cents  ?  for  fifty  cents  ?  for  seventy  cents  ? 
for  ninety  cents  ? 

If  there  are  twenty  quires  of  paper  in  a  ream,  how  many 
reams  are  there  in  forty  quires  ?  in  sixty  quires  ?  in  eighty 
quires  ? 

If  twenty  things  make  a  score,  how  many  scores  are 
there  in  forty  ?  in  one  hundred  ? 

If  thirty  days  are  counted  to  a  month,  how  many  months 
will  sixty  days  equal  ?  will  ninety  days  equal  ? 

For  eighty  cents,  how  many  pictures  can  I  have  framed 
at  forty  cents  apiece  ? 

One  hundred  is  how  many  times  twenty  ?  is  how  many 
times  fifty  ? 

Ninety  is  how  many  times  thirty  ? 

Sixty  is  how  many  times  thirty?  is  how  many  times 
twenty  ? 

Eighty  is  how  many  times  twenty ;  is  how  many  times 
forty? 

Take  this  number  work  : 


20-10  = 

20- 

-10  = 

20- 

-    2  = 

10  X    4  = 

30  - 10  = 

30- 

-10  = 

50- 

-    5  = 

10  X    2  = 

40-10  = 

60- 

-10  = 

70- 

-   7  = 

lOx    3  = 

50-10  = 

40- 

-10  = 

30- 

-   3  = 

10  X    5  = 

60  - 10  = 

70- 

-10  = 

40- 

-   4  = 

10  X    7  = 

70-10  = 

50- 

-10  = 

60- 

-   6  = 

10  X    9  = 

80  - 10  = 

80- 

-10  = 

80- 

-   8  = 

10  X    8  = 

90  - 10  = 

100- 

-10  = 

100- 

-10  = 

10x10  = 

TENS.  321 


90 

90 

90 

90 

90 

90 

-30 

-50 

-70 

-60 

-40 

-20 

80 

80 

80 

80 

80 

80 

-30 

-50 

-70 

-60 

-40 

-20 

70 

70 

70 

70 

70 

70 

-30 

-50 

-20 

-40 

-60 

-30 

If  you  have  two  ten-cent  pieces  and  a  cent,  how  much 
money  have  you  ?  If  your  cent  were  a  two-cent  piece,  how 
much  money  would  you  have?  If  you  had  a  three-cent 
piece  instead  of  a  one-cent  piece,  how  much  money  would 
you  have  ?  Suppose  you  had  two  two-cent  pieces,  and  the 
twenty  cents,  how  much  money  would  you  have  ?  If  you 
had  a  five-cent  piece  and  twenty  cents,  how  much  money 
would  you  have  ?  What  part  of  a  dollar  would  you  have  ? 
How  many  cents  are  twenty  cents  and  two  three-cent 
pieces?  twenty  cents  and  three  two-cent  pieces?  twenty 
cents,  a  five-cent  piece,  and  a  two-cent  piece  ?  twenty  cents, 
a  five-cent  piece,  and  a  three-cent  piece  ?  twenty  cents  and 
three  three-cent  pieces  ? 

Express  the  sum  of : 

Twenty  and  one.  Twenty  and  five. 

Twenty  and  two.  Twenty  and  seven. 

Twenty  and  six.  Twenty  and  nine. 

Twenty  and  three.  Twenty  and  eight. 

If  twenty  and  one  are  twenty-one,  how  much  are  thirty 
and  one  ? 


322  FIRST  STEPS   IN   NUMBER. 

Express  : 

Thirty  and  one.  Forty  and  one. 

Thirty  and  four.  Forty  and  four. 

Thirty  and  six.  Forty  and  six. 

Thirty  and  eight.  Forty  and  eight. 

Thirty  and  five.  Forty  and  five. 

Thirty  and  nine.  Forty  and  nine. 

Thirty  and  two.  Forty  and  two. 

Fifty  and  one.  Sixty  and  one. 

Fifty  and  two.  Sixty  and  two. 

Fifty  and  five.  Sixty  and  six. 

In  twenty-four  how  many  tens  ?  how  many  ones  besides  ? 
In  thirty-five  how  many  tens  and  how  many  ones  besides  ? 
in  fifty-seven  ?  in  sixty -three  ?  in  seventy-four  ?  in  eighty- 
nine  ?  in  ninety-six  ?  in  seventeen  ?  in  fifteen  ?  in  nineteen  ? 

Write  in  a  column  :  Thirty-seven  ;  forty-one  ;  sixty-three  ; 
eighty -five  ;  fifty-four  ;  seventy-seven.  Show  me  the  column 
of  ones ;  the  column  of  tens.  Which  number  has  the  most 
tens? 

Copy  and  complete : 


20  +  3  = 

10  +  2  = 

12-2  = 

7  +  10  = 

20  +  5  = 

20  +  2  = 

22-2  = 

17+10  = 

20  +  7  = 

30  +  2  = 

32-2  = 

27  +  10  = 

20  +  9  = 

40  +  2  = 

42-2  = 

37  + 10  = 

30  +  4  = 

50  +  2  = 

52-2  = 

47  + 10  = 

30  +  7  = 

60  +  2  = 

62-2  = 

57  + 10  = 

80  +  2  = 

70  +  2  = 

72-2  = 

67  +  10  = 

40  +  1  = 

80  +  2  = 

82-2  = 

77  +  10  = 

40  +  8  = 

90  +  2  = 

92-2  = 

87  + 10  = 

50  +  4  = 

10+7  = 

14  -  4  = 

97-10  = 

CHAPTER  XXI. 

THE    NUMBER    TWENTY. 


§  43.    The  Number  Twenty. 

Take  twenty.     How  many  tens  have  you  taken  ? 

Two  tens  are  how  many.    Express  this  fact  on  the  board  ? 

Show  me  one-half  of  twenty.  What  is  one-half  of  twenty  ? 
Express :  One-half  of  twenty  is  ten. 

If  there  are  twenty  pencils  on  my  desk,  and  half  are  lead- 
pencils  and  half  are  slate-pencils,  how  many  pencils  of  each 
kind  are  on  my  desk  ? 

If  there  are  twenty  pins  in  a  row,  how  many  pins  are  in 
half  of  the  row  ? 

I  am  twenty  years  old.  Who  knows  some  little  girl  who 
is  half  as  old  as  I  am  ?     How  old  is  she  ? 

Our  school  term  is  twenty  weeks  long.  If  we  have  a 
vacation  when  half  the  term  is  over,  how  many  weeks  after 
the  beginning  of  the  term  does  vacation  come  ? 

Who  can  express :  Twenty  divided  by  ten  ? 

Give  me  an  example  for  twenty  divided  by  ten. 

Express  on  the  board  :  Ten  and  ten  are  twenty.  What 
two  equal  numbers  make  ten  ?  Write  :  Five  and  five  under 
each  ten.  Kead  :  Ten  and  ten  are  twenty,  in  fives.  (Five 
and  five  and  five  and  five  are  twenty.)  How  many  fives 
are  twenty  ?     Express  :  Four  fives  are  twenty. 

Four  five-cent  pieces  are  how  much  money  ? 


324  FIRST  STEPS  IN   NUMBER: 

Four  gloves  have  how  many  fingers  ? 

A  dog  has  how  many  toes  ? 

Four  pansy  blossoms  have  how  many  petals  ? 

Four  five-cent  bunches  of  envelopes  will  cost  how  much? 

Into  how  many  fives  can  twenty  be  divided  ?  Express 
this  fact. 

Give  an  example  for :  Twenty  divided  by  five. 

What  four  equal  numbers  make  twenty  ? 

What  part  of  twenty  is  each  of  these  numbers  ? 

What  part  of  twenty  is  five  ? 

Express  :  One-fourth  of  twenty  is  five. 

I  had  twenty  quires  of  paper  done  up  in  four  equal 
packages.     How  many  quires  were  in  each  package  ? 

A  little  girl  who  had  two  dimes  spent  a  fourth  of  her 
money  for  fancy  crackers.    How  much  money  did  she  spend  ? 

If  I  am  twenty  years  old,  how  old  is  a  little  girl  who  is 
only  one-fourth  of  my  age  ? 

Copy  and  complete : 


2x10  = 

20-^    5  = 

X    5=20 

-^10=  2 

20^10  = 

iof20  = 

^   5=   4 

9x        =18 

|of20  = 

10  +  10  = 

of  20  =  10 

6x        =18 

4x    5  = 

15+    5  = 

of  20=    5 

5x        =15 

20         18 
-10       -9 

16 
-8 

14 

-7 

19          17 
- 13     - 12 

18          20 
- 15     - 15 

3 
2 
5 
4 
3 

4 
3 
2 
3 
6 

6 
5 
3 

2 
4 

3 
4 
5 
2 
6 

THE  NUMBER  TWENTY.  325 

Who  knows  how  many  fours  there  are  in  twenty  ?  Those 
who  do  not  know  must  find  out  with  the  splints. 

Express  :  Twenty  divided  by  four  are  five. 

How  many  barges  will  twenty  horses  supply  if  four  are 
required  for  each  barge  ? 

Twenty  horse-shoes  will  shoe  how  many  horses  all  round  ? 

How  many  quarts  of  milk  can  be  bought  for  twenty  cents 
if  each  quart  costs  four  cents  ? 

Twenty  quarts  are  how  many  gallons? 

Twenty  gills  are  how  many  pints  ? 

If  you  find  five  fours  in  twenty,  how  many  fours  must 
you  put  together  to  make  twenty  ? 

Express  :  Five  fours  are  twenty. 

How  many  wheels  have  five  wagons  ? 

How  many  legs  have  five  chairs  ? 

How  many  sides  have  five  squares  ? 

Five  gallons  are  how  many  quarts  ? 

Five  pints  are  how  many  gills  ? 

Five  horses  wear  how  many  shoes  ? 

How  many  twos  in  ten  ?  How  many  twos  in  two  tens  ? 
How  many  twos  in  twenty,  then  ? 

Express  :  Twenty  divided  by  two  are  ten. 

If  you  have  twenty  cents  in  two-cent  pieces,  how  many 
two-cent  pieces  have  you  ? 

Twenty  pints  are  how  many  quarts  ? 

Twenty  half-dollar  pieces  make  how  many  dollars  ? 

Twenty  slate-pencils  will  cost  how  much  if  two  can  be 
bought  for  a  cent  ?  Twenty  apples  will  cost  how  much  at 
the  same  rate  ? 

How  many  dozen  buttons,  at  two  cents  a  dozen,  can  be 
bought  for  twenty  cents  ? 

If  in  twenty  you  find  ten  twos,  how  many  twos  will  you 
take  to  make  twenty  ? 

Ten  two-cent  pieces  are  how  much  money  ? 


326  FIRST  STEPS   IN   NUMBER. 

Ten  boys  have  how  many  ears  ? 

Ten  boys  wear  how  many  shoes  ?  how  many  mittens  ? 
How  much  does  it  cost  to  send  ten  letters  through  the 
mail,  if  it  costs  two  cents  for  each  letter  ? 
Ten  quarts  are  how  many  pints  ? 
Ten  dollars  are  how  many  half-dollars  ? 


Illustrate  these  examples,  and  tell  me  the  answer  : 

A  basket-maker  put  two  handles  on  each  basket.  How 
many  handles  did  he  put  on  ten  baskets  ? 

I  have  two  boxes,  both  the  same  size.  They  are  three 
inches  in  length  and  two  in  width.  How  many  inches  of 
gilt  paper  will  it  take  to  bind  both  boxes  around  the  edge  ? 

I  made  five  gallons  of  preserves,  and  put  the  preserves 
into  quart  jars.     How  many  jars  did  I  use  ? 

I  have  a  square  garden  plot  bordered  with  foliage  plants. 
If  there  are  four  on  each  side,  one  standing  at  each  corner, 
how  many  plants  are  around  the  plot  ? 

Make  a  triangle  with  dots,  putting  a  dot  on  each  corner, 
and  having  three  dots  on  each  side.  How  many  dots  have 
you  made  ?  Make  believe  these  are  trees  arranged  to  form 
an  arbor.  How  many  trees  does  it  take  to  form  a  triangle 
if  there  are  three  on  each  side  ? 

How  many  trees  will  it  take  to  form  a  square,  if  there  are 
five  trees  on  each  side  ?  if  there  are  six  trees  on  each  side  ? 

Take  this  number  work  : 

20-4--                 16+    4=  iof20  = 

5x4=                15+    5=  5x       =20 

20-^2=                18+2=  4x       =20 

10x2=                  i-of20=  10  X       =20 


THE 

NUMBER 

TWENTY. 

327 

2x 

=  20 

20-^ 

=  1 

+ 

5  = 

=  20 

20  H- 

=  5 

X 

5 

=  20 

+ 

4  = 

=  20 

20-^ 

=  4 

X 

4 

=  20 

+  10  = 

=  20 

20-^ 

=  2 

X 

10 

=  20 

+ 

2  = 

=  20 

20-5- 

=  10 

X 

2 

=  20 

of  20  = 

=  5 

10 

10 

10 

10 

10 

10 

2 

3 

4 

5 

6 

7 

10 

10 

10 

20 

20 

20 

8 

9 

10 

1 

2 

3 

20 

20 

80 

30 

40 

50 

4 

5 

2 

3 

2 

2 

10 

20 

30 

40 

50 

60 

-3 

-3 

. 

-3 

-3 

-3 

-3 

10 

20 

30 

40 

50 

60 

-7 

-7 

-7 

-7 

-7 

-7 

Add: 

5 

6 

7 

6 

9 

8 

6 

12 

6 

8 

4 

3 

5 

8 

4 

7 

5 

8 

12 

9 

CHAPTER  XXII. 

THE  NUMBER  TWENTY-ONE. 


§  44.    The  Number  Twenty-One. 

I  have  six  three-cent  pieces;  how  much  money  have  I? 
If  you  give  me  another  three-cent  piece,  how  much  money 
shall  I  have  ?  How  many  three-cent  pieces  shall  I  have  ? 
Seven  three-cent  pieces  are  how  much  money  then  ? 

Seven  oranges  at  three  cents  each  will  cost  how  much  ? 

In  seven  yards  of  rope  how  many  feet  of  rope  ? 

Seven  triangles  have  together  how  many  sides  ? 

Seven  three-cornered  hats  with  a  tassel  on  each  corner 
have  together  how  many  tassels  ? 

If  it  takes  three  yards  of  ribbon  for  one  pair  of  bonnet- 
strings,  how  many  yards  of  ribbon  will  be  required  for 
seven  pairs  of  bonnet-strings  ? 

If  Willie's  hens  lay  three  eggs  a  day,  how  many  eggs  will 
they  lay  in  a  week  ? 

Express :  Seven  threes  are  twenty-one. 

If  you  must  put  seven  threes  together  to  make  twenty- 
one,  how  many  threes  can  you  find  in  twenty-one  ? 

Twenty-one  feet  of  chain  are  equal  to  how  many  yards 
of  chain  ? 

Twenty-one  cents  will  buy  how  many  three-cent  pencils  ? 

If  I  cut  a  strip  of  paper  that  is  twenty-one  inches  long 
into  pieces  tibree  inches  long,  into  how  many  pieces  shall  I 
cut  the  strip  of  paper  ? 


THE   NUMBER   TWENTY-ONE.  329 

How  many  three-cent  books  can  be  bought  for  twenty- 
one  cents? 

If  the  news-boy  sells  seven  papers  at  three  cents  apiece, 
how  many  cents  does  he  receive  for  the  papers  ?  If  he  is 
allowed  to  keep  one  cent  for  each  paper  he  sells,  how  many 
cents  must  he  return  to  his  employer?  Fourteen  and 
seven  then  are  how  many  ? 

How  many  sevens  make  fourteen?  and  since  fourteen 
and  seven  are  twenty-one,  how  many  sevens  make  twenty- 
one? 

In  three  weeks  how  many  days  ? 

If  there  are  three  groups  of  stars  and  seven  stars  in  each 
group,  how  many  stars  are  in  the  tlwee  groups  ? 

Three  pounds  of  beef  at  seven  cents  a  pound  will  cost 
how  much  ? 

Three  pairs  of  horses  at  seven  hundred  dollars  a  pair 
will  cost  how  many  hundred  dollars  ? 

Express  :  Three  sevens  are  twenty-one. 

If  three  sevens  make  twenty-one,  into  how  many  sevens 
can  twenty-one  be  divided  ?  Twenty-one  cents  then  will 
buy  how  many  seven-cent  Joaves  of  bread?  how  many 
seven-cent  copy-books? 

If  berries  are  seven  cents  a  quart,  how  many  quarts  can 
be  bought  for  twenty-one  cents  ? 

In  twenty-one  days  from  to-day  I  shall  go  home.  How 
many  Sundays  before  I  go  home  ?     How  many  Mondays  ? 

Twenty-one  children  received  stars  for  singing  nicely. 
Each  seven  received  a  different  colored  star.  How  many 
different  stars  were  given  out  ? 

Express :  Twenty-one  divided  by  seven  are  three. 

What  three  equal  numbers  make  twenty-one  ? 

What  then  is  one-third  of  twenty-one  ? 

If  twenty-one  nuts  were  divided  equally  among  three 
boys,  how  many  nuts  did  each  boy  receive? 


330  FIRST   STEPS    IN   NUMBER. 

A  man  wtio  owed  twenty-one  dollars  agreed  to  pay  a 
third  of  the  debt  each  month  until  it  was  paid.  How 
much  money  did  he  pay  each  month  ? 

If  a  bicycle  will  travel  twenty-one  miles  in  three  hours, 
at  what  rate  is  that  per  hour  ? 

Express :  One-third  of  twenty-one  is  seven. 

Count  by  threes  to  twenty-one. 

Count  by  sevens  to  twenty-one. 

Express:  Eighteen  and  three ;  four  and  seven;  fourteen 
and  seven ;  eight  and  three ;  twenty-one  minus  three ; 
eleven  minus  three ;  twenty-one  minus  seven ;  eleven 
minus  seven. 


Fill  out : 

7x    3  = 

21-7  = 

X3  =  21 

+   3  =  21 

21^   8  = 

21-3  = 

X7  =  21 

+    7  =  21 

3x    7  = 

14  +  7  = 

-^7=   3 

+ 10  =  21 

21^    7  = 

18  +  3  = 

-^3=   7 

+  20  =  21 

J  of  21  = 

20+1  = 

-7  =  14 

-   3=18 

Review   Exercise. 

Cloth  that  is  a  yard  and  a  foot  wide  is  how  many  feet 
wide? 

If  a  sail  cloth  is  seven  yards  long,  how  many  feet  long 
is  it? 

If  a  ship  has  twenty-one  feet  of  rope  in  one  line,  how 
many  yards  long  is  the  line? 

How  many  days  in  a  school  week  ? 

How  many  days  in  four  school  weeks  ? 

If  a  dog  has  four  toes  on  each  foot,  how  many  toes  has  he 
altogether? 

If  a  squirrel  has  five  toes  on  each  fore-foot,  how  many 
toes  have  two  squirrels  on  their  fore-feet  ? 


THE   NUMBER   TWENTY-ONE.  331 

If  a  cat  lias  five  toes  on  each  fore-foot,  how  many  toes 
have  two  cats  on  their  fore-feet  ? 

A  cat  has  four  toes  on  each  hind  foot  and  ^ye  toes  on 
each  fore-foot.     How  many  toes  has  she  altogether? 

If  I  cut  ribbon  which  is  eighteen  inches  long  into  pieces 
six  inches  long,  how  many  such  pieces  shall  I  have? 

In  twenty-one  days  how  many  Sundays?  how  many  Fri- 
days ?  how  many  Saturdays  ? 

How  many  gills  in  a  quart  ?  How  many  gills  in  two 
quarts  ? 

If  you  go  to  school  nine  months  in  a  year,  how  many 
months  do  you  go  to  school  in  two  years  ? 

If  one  spider  has  nine  eyes,  how  many  eyes  have  two 
spiders  ? 

If  one  parasol  has  ten  ribs,  how  many  ribs  have  two  par- 
asols ?  three  parasols  ?  seven  parasols  ? 

Name  a  number  made  up  of  ten  and  four ;  of  ten  and 
eight ;  of  ten  and  two ;  of  ten  and  seven ;  of  four  tens  and 
seven  ;  of  six  tens  and  six ;  of  seven  tens  and  nine  ;  of  nine 
tens  and  two  ;  of  eight  tens  and  five ;  of  five  tens  and 
eight;  of  three  tens  and  nine  ;  of  two  tens  and  one. 

If  there  are  three  books  on  one  shelf,  and  five  times  as 
many  books  on  another  shelf,  how  many  books  are  on  the 
second  shelf? 

If  I  slide  down  hill  ten  times,  and  you  slide  down  hill 
twice  as  many  times,  how  many  times  do  you  slide  down 
hill? 

If  I  have  to  walk  a  fourth  of  a  mile  to  school,  and  you 
have  to  walk  three  times  as  far,  what  part  of  a  mile  do  you 
walk  to  school  ? 

If  you  have  one-third  of  a  dollar,  and  I  have  twice  as 
much  money,  how  many  thirds  of  a  dollar  do  I  have? 

If  a  family  eats  a  quarter  of  a  lamb  each  week  for  four 
weeks,  how  many  quarters  of  lamb  does  the  family  eat  ? 


332  FIRST  S.TEPS   IN  .NUMBER. 

If  it  takes  a  sixth  of  a  yard  of  ribbon  to  make  one  loop, 
how  much  ribbon  will  it  take  for  four  loops? 

If  you  have  one-eighth  of  a  dollar,  and  I  have  eight 
times  as  much  money,  how  much  money  do  I  have  ? 

How  many  two-cent  cakes  can  you  buy  for  five  cents, 
and  how  many  cents  will  you  have  left  ?  for  seven  cents, 
and  what  will  you  have  left  ?  for  nine  cents  ?  for  seventeen 
cents?  for  nineteen  cents  ?  for  twenty-one  cents?  for  twenty- 
three  cents  ? 

How  many  three-cent  pencils  can  you  buy  for  four  cents, 
and  how  many  cents  will  you  have  left  ?  for  ^ye  cents,  and 
how  much  will  you  have  left  ?  for  eight  cents  ?  for  eleven 
cents?  for  sixteen  cents?  for  nineteen  cents?  for  twenty- 
three  cents? 

How  many  fours  and  what  else  make  nine  ?  make  thir- 
teen? make  eighteen?  make  twenty-one?  make  twenty- 
two? 

Eleven  divided  by  five  gives  what  answer?  Thirteen 
divided  by  five  gives  what  answer?  Sixteen  divided  by 
five?  eighteen  divided  by  fiYe?  twenty-one  divided  by  five? 
twenty-three  divided  by  five  ? 

Divide  eight  by  six.  Divide  by  six  :  nine  ;  ten  ;  eleven ; 
fourteen ;  sixteen  ;  nineteen  ;  twenty-one  ;  twenty-three. 

Copy  and  complete: 


7  = 

3x2  + 

19  =  6x3  + 

7=1x5+ 

9  = 

4x2  + 

23  =  7  X  3  + 

9=1x5+ 

13  = 

6x2  + 

7=1x4+ 

13  =  2  X  5  + 

17  = 

8x2  + 

11  =  2x4  + 

17  =  3x5  + 

21  = 

10X2  + 

15  =  3x4  + 

21  =  4  X  5  + 

5  = 

1X8  + 

17  =  4x4  + 

8=1X6+ 

7  = 

2X3  + 

19  =  4x4  + 

13  =  2  X  6  + 

11  = 

8x3  + 

21  =  5x4  + 

,15  =  2  X  6  + 

CHAPTEE    XXIII. 

THE   NUMBER  TWENTY-FOUR. 


§  45.     The  Number  Twenty-Four. 

If  I  have  seven  three-cent  pieces,  how  much  money  do 
I  have  ?  If  I  earn  another  three-cent  piece,  how  much 
money  shall  I  have  ?  .Eight  three-cent  pieces,  then,  are 
how  much  money  ? 

Eight  three-cent  postage  stamps  will  cost  how  much  ? 
Eight  three-cent  pencils  ?  Eight  oranges  at  three  cents 
apiece  ? 

Eight  clover  leaves  have  how  many  leaflets  ? 

Eight  chestnut  burrs  contain  how  many  nuts,  if  there 
are  three  nuts  in  each  burr  ? 

Eight  yards  of  curtain-cord  are  how  many  feet  of  cur- 
tain-cord ? 

If  a  blackboard  consists  of  eight  slates,  each  a  yard  long, 
how  many  feet  long  is  the  blackboard  ? 

It  takes  three  yards  of  cloth  to  make  a  jacket.  How 
many  yards  of  cloth  are  required  for  eight  jackets  ? 

Express  :  Eight  threes  are  twenty-four. 

Who  knows  into  how  many  threes  we  can  divide  twenty- 
four  ? 

When  lemons  are  three  cents  apiece,  how  many  lemons 
can  be  bought  for  twenty-four  cents  ? 

A  stick  that  is  twenty -four  feet  long  can  be  cut  into  how 
many  yard-sticks  ? 


334  FIRST   STEPS   IN    NUMBER. 

A  farmer's  wife,  who  has  twenty-four  pounds  of  butter 
to  make  into  balls,  puts  three  pounds  in  each  ball.  How 
many  balls  of  butter  does  she  make  ? 

A  market-man  measured  out  twenty-four  quarts  of  ber- 
ries with  a  three-quart  measure.  How  many  times  did  he 
fill  the  measure  ? 

Express :  Twenty-four  divided  by  three  are  eight. 

What  eight  equal  numbers  make  twenty-four  ? 

What  part,  then,  of  twenty-four  is  three  ? 

If  I  divide  twenty-four  apples  equally  among  eight 
boys,  how  many  apples  shall  I  give  to  each  boy  ? 

A  man  bought  eight  chairs  for  twenty-four  dollars.  What 
was  the  cost  of  each  chair  ? 

I  put  twenty-four  pears  away  in  the  drawer  to  ripen,  but 
an  eighth  of  the  number  decayed.     How  many  decayed  ? 

This  line  is  twenty-four  inches  long.  How  long  is  one- 
eighth  of  the  line  ? 

There  are  twenty-four  hours  in  a  day.  How  long  is 
one-eighth  of  the  day  ? 

Jennie  has  twenty-four  examples  to  do.  When  she  has 
done  three,  what  part  of  the  number  has  she  done  ? 

Express  :  One-eighth  of  twenty-four  is  three. 

Five  fours  are  how  many  ?  Another  four  will  make  how 
many  ?     How  many  fours  make  twenty-four,  then  ? 

Six  squares  have  how  many  corners  ? 

Six  horses  have  how  many  legs  ? 

Six  dogs  have  how  many  legs  ? 

Six  gallons  of  oysters  are  how  many  quarts  of  oysters  ? 

Six  four-quart  pails  will  hold  how  many  quarts  of  syrup  ? 

Six  pints  of  yeast  are  equal  to  how  many  gills  of  yeast  ? 

I  bought  six  yards  of  silk  at  four  dollars  a  yard.  How 
much  did  I  pay  for  the  silk  ? 

My  little  brother  is  four  years  old,  I  am  six  times  as 
old  as  he.     How  old  am  I  ? 


THE   NUMBER  TWENTY-FOUR.  335 

It  is  four  miles  to  Newtown,  and  six  times  as  far  to  Old- 
town.     How  far  is  it  to  Oldtown  ? 

Express  :  Six  fours  are  twenty-four. 

A  cliair-maker  turned  out  twenty-four  chair  legs.  How 
many  chairs  would  they  supply  ? 

In  twenty-four  gills  how  many  pints  ? 

In  twenty-four  quarts  how  many  gallons  ? 

There  were  twenty-four  buttons  on  a  card,  four  in  each 
row.     How  many  rows  of  buttons  were  there  ? 

Here  are  twenty-four  splints  of  equal  length.  How  many 
separate  squares  can  you  form  from  them  ? 

Express :  Twenty-four  divided  by  four  are  six. 

What  six  equal  numbers  make  twenty-four  ? 

What,  then,  is  one-sixth  of  twenty-four  ? 

If  you  have  twenty-four  buttons,  and  use  a  sixth  of  them 
for  your  boot,  how  many  buttons  do  you  use  ?  How  many 
buttons  will  you  have  left  ? 

A  man  who  owned  twenty-four  acres  of  land  planted 
one-sixth  of  it  with  potatoes.  How  many  acres  of  potatoes 
did  he  plant  ? 

He  planted  another  sixth  of  the  land  with  corn.  How 
many  acres  of  corn  had  he  ? 

If  you  earn  twenty-four  cents  a  week,  what  do  you  earn 
in  a  day. 

The  cook  used  twenty-four  eggs  in  making  six  loaves  of 
cake.     How  many  eggs  did  she  use  for  each  loaf? 

Express  :  One-sixth  of  twenty-four  is  four. 

Give  me  a  story  for  any  fact  in  twenty-four  which  you 
have  learned. 

Tell  me  the  answer  as  I  point  to  each  blank :  — 

8x3-=  6x4=        20+    =24:  24-  =20 

24 --3=         24 -f- 4=        21+    =24  24-  =18 

4  of  24=        iof24=        18+    =24  24-  =21 


336  FIRST  STEPS   IN  NUMBER. 

Three  sixes  are  how  many  ?  Another  six  will  make  how 
many  ?     How  many  sixes  make  twenty-four  ? 

How  many  dollars  will  a  man  earn  in  four  weeks,  if  he 
earns  a  dollar  a  day  ? 

If  you  go  to  school  six  days  in  a  week,  how  many  days 
will  you  go  to  school  in  four  weeks  ? 

How  many  links  in  a  chain  that  is  four  feet  long,  if  there 
are  six  links  in  each  foot  of  the  chain  ? 

What  will  four  car-fares  cost  at  six  cents  a  fare  ? 

If  six  persons  can  sit  on  one  settee,  how  many  persons 
can  sit  on  four  settees  ? 

Express  :  Four  sixes  are  twenty-four. 

Who  has  a  story  for  twenty-four  divided  by  six  ? 

If  eggs  are  packed  in  layers  of  half  a  dozen  each,  how 
many  layers  will  twenty-four  eggs  make  ? 

How  many  quarts  of  milk  at  six  cents  a  quart  can  be 
bought  for  twenty-four  cents  ? 

How  many  window  draperies  can  be  made  from  twenty- 
four  yards  of  goods,  if  six  yards  are  required  for  one  win- 
dow? 

Express :  Twenty-four  divided  by  six  are  four. 

If  twenty-four  is  divided  into  four  equal  groups,  how 
many  are  in  each  group  ?  What  part  of  twenty-four  is 
each  group  ?     What  is  one-fourth  of  twenty-four  ? 

If  four  oranges  cost  twenty-four  cents,  what  will  one 
orange  cost  ? 

If  four  lamp-chimneys  cost  twenty-four  cents,  what  will 
one  lamp-chimney  cost  ? 

A  boy  who  had  twenty-four  cents  spent  a  fourth  of  his 
money  for  a  balloon.     How  much  money  had  he  left  ? 

There  are  twenty-four  hours  in  a  day.  How  many  hours 
in  a  fourth  of  the  day  ? 

If  the  time  between  breakfast  and  dinner  is  a  fourth 
of  the  day,  how  many  hours  is  it  between  breakfast  and 
dinner  ? 


THE   NUMBER   TWENTY-FOUR.  337 

If  I  am  in  school  a  fourth  of  the  day,  how  many  hours 
am  I  in  school  ? 

If  papa  goes  to  work  at  seven  o'clock,  and  comes  home  at 
one  o'clock,  what  part  of  the  day  has  he  been  at  work? 

There  are  twenty-four  sheets  of  paper  in  a  quire  of  paper. 
How  many  sheets  in  a  quarter  of  a  quire  ?  If  paper  is 
twenty-four  cents  a  quire,  what  will  a  sheet  of  paper  cost  ? 
What  will  a  fourth  of  a  quire  cost  ? 

A  quire  of  paper  is  usually  put  up  in  four  equal  lots. 
How  many  sheets  of  paper  in  each  lot  ? 

Express  :  One-fourth  of  twenty-four  is  six. 

Write :  Twenty-four  sheets  of  paper  make  a  quire  of 
paper. 

Which  are  more,  eight  threes  or  three  eights?  Eight 
threes  are  how  many  ?     Then  three  eights  are  how  many  ? 

Six  fours  are  equal  to  how  many  eights  ?  Six  fours  are 
how  many  ?     Then  three  eights  are  how  many  ? 

Who  has  an  example  for  :  Three  eights  are  twenty -four  ? 

Three  oxen  wear  how  many  shoes  ? 

Three  hens  have  how  many  toes  ? 

How  many  wheels  have  three  passenger-cars? 

Three  pairs  of  horses  need  shoeing  all  round.  How 
many  shoes  will  be  required  to  shoe  them  ? 

Express  :  Three  eights  are  twenty-four. 

If  you  should  arrange  twenty-four  books  on  a  book-case, 
putting  eight  books  on  each  shelf,  how  many  shelves  would 
it  take  ? 

Twenty-four  cents  will  buy  how  many  loaves  of  bread 
at  eight  cents  a  loaf?  How  many  yards  of  cambric  at 
eight  cents  a  yard  ? 

Twenty-four  quarts  of  molasses  will  fill  how  many  two- 
gallon  jugs? 

Twenty-four  gills  of  jelly  will  make  how  many  quarts  of 
jelly? 


338 


FIRST  STEPS   IN   NUMBER. 


Express :  Twenty-four  divided  by  eight  are  three. 

What  three  equal  numbers  make  twenty-four  ? 

What  then  is  one-third  of  twenty-four  ? 

A  boy  who  had  twenty-four  brackets  for  sale,  sold  one- 
third  of  them.     How  many  did  he  sell  ? 

There  were  twenty-four  spoons  in  the  spoon-holder. 
We  used  a  third  of  them  at  tea.  How  many  spoons  re- 
mained in  the  spoon-holder  ? 

I  had  a  quire  of  paper,  but  have  used  a  third  of  it. 
How  many  sheets  have  I  used  ? 

Allen  sleeps  a  third  of  the  day,  works  a  third  of  the 
day,  and  spends  the  rest  of  his  time  in  amusement.  How 
many  hours  has  he  for  amusement  ? 

Express  :  One-third  of  twenty-four  is  eight. 

Take  this  number  work  : 


24^    8  = 

3x8  = 

24- 

3  = 

3x    8  = 

8x3  = 

24- 

4  = 

iof24  = 

4x6  = 

24- 

6  = 

24^    6  = 

6x4  = 

24- 

8  = 

4X    6  = 

24-^3  = 

8x 

=  24 

iof24  = 

24^8  = 

6x 

=  24 

24-^   4  = 

24-^-4  = 

3x 

=  24 

6x    4  = 

24-^-6  = 

4x 

=  24 

iof24  = 

10  +  4  = 

24-^ 

=   8 

24-^    3  = 

20  +  4  = 

24^ 

=   4 

8x    3  = 

11  +  3  = 

24  H- 

=   6 

iof24  = 

21  +  3  = 

24- 

=    8 

iof24  = 

8  +  6  = 

of24=    6 

iof24  = 

18+6  = 

of  24=  4 

iof24  = 

6  +  8  = 

of  24=    3 

|of24  = 

16  +  8  = 

of  24=    8 

THE   NUMBER  TWENTY-FOUR.  339 


24 

24 

24 

14 

24 

14 

-10 

-12 

-8 

-8 



-6 

_ 

-6 

3 

4 

3 

2 

3 

4 

4 

5 

3 

2 

8 

4 

6 

4 

8 

6 

3 

3 

3 

3 

4 

5 

4 

4 

7 

8 

6 

7 

5 

9 

One-fifth. 

Into  how  many  parts  have  I  cut  the  circle?  (Five.) 
How  do  the  parts  compare  in  size  ?  (Equal.)  Who  knows 
what  part  of  the  whole  circle  each  one  of  these  five  equal 
parts  is  ?     Show  me  then  one-fifth  of  the  circle. 

You  may  draw  a  line  on  the  board,  and  divide  it  into 
fifths. 

Divide  this  triangle  into  fifths  by  drawing  lines  from  the 
vertex  to  the  base. 

What  number  can  you  divide  into  fifths  and  have  or\i 
for  each  fifth?  What  number  can  you  divide  and  hav« 
two  for  each  fifth  ?  What  number  has  three  in  each  fifth  ? 
What  five  equal  numbers  make  twenty  ?  Then  what  is 
one-fifth  of  twenty  ? 

If  I  give  you  two  two-cent  pieces,  and  tell  you  th^c  is 
one-fifth  of  the  money  I  have,  can  you  tell  me  how  much 
money  I  have  ?  Suppose  I  give  you  a  three-cent  piece,  and 
tell  you  that  is  one-fifth  of  the  money  I  have ;  can  you  tell 
me  how  much  money  I  have  ? 

Two  is  one-fifth  of  what  number  ? 

How  many  fifths  make  a  whole  ? 


CHAPTER  XXIV. 

THE  NUMBER  TWENTY-FIVE. 


§  46.     The  Number  Twenty-Five. 

Twenty  and  five  are  how  many  ?  How  many  fives  make 
twenty  ?     Twenty  and  five  then  are  how  many  fives  ? 

Express :  Five  fives  are  twenty-five. 

How  many  school-days  in  five  weeks  ? 

How  many  fingers  have  five  gloves  ? 

Five  bureaus,  with  five  drawers  in  each  bureau,  have 
how  many  drawers  together  ? 

How  many  feet  of  linen  must  I  buy  for  five  window- 
shades  if  each  shade  must  be  five  feet  long  ? 

Each  think  of  an  example  for :  Five  times  five  are 
twenty-five. 

Each  think  of  an  example  for:  Twenty-five  divided  by 
five. 

What  is  one  of  the  five  equal  numbers  which  make 
twenty-five  ?     What  part  of  twenty-five  is  five  ? 

If  I  had  a  quarter  of  a  dollar,  and  you  had  one-fifth  as 
much  money,  what  piece  of  money  would  you  have  ?  If 
you  had  two-fifths  as  much  money,  what  piece  of  money 
would  you  have  ?  If  you  had  three-fifths  as  much  money, 
what  two  pieces  of  money  would  you  have  ?  If  you  had 
four  five-cent  pieces,  what  part  of  my  quarter  of  a  dollar 
would  you  have  ? 

How  many  five-cent  pieces  must  you  have  to  equal  my 
quarter  ? 


THE   NUMBER   TWENTY-FIVE.  34:1 

Give  an  example  for :  One-fifth  of  twenty-five  is  five. 

Express:  One-fifth  of  twenty-five  is  five. 

Tell  me  what  number  is  needed  in  each  blank : 


5x    5  = 

|of20  = 

i  +  i  =  ir- 

25-=-   5  = 

iofl5  = 

f  +  i  =  ^. 

|of25  = 

ioflO  = 

|  +  |  =  ? 

Exercise  for  Review. 

How  many  pints  in  a  quart  ?  How  many  pints  in  two 
quarts  ?  four  quarts  ?  six  quarts  ?  eight  quarts  ?  ten  quarts  ? 
eleven  quarts  ?  twelve  quarts  ? 

Eleven  two-cent  pieces  are  how  much  money  ?  Eleven 
pairs  of  scissors  have  how  many  blades  ?  Eleven  sheets  of 
paper  have  how  many  leaves?  Eleven  books  have  how 
many  covers? 

Express  :  Eleven  twos  are  twenty-two.  '    ' 

Here  are  some  blocks,  each  two  inches  thick.  If  eleven 
blocks  are  piled  up,  one  top  of  the  other,  how  high  will 
the  pile  be? 

This  stick  is  two  feet  long.  Eleven  such  sticks  placed 
end  to  end  would  extend  how  many  feet?  How  many 
yards  ?  Twelve  sticks  placed  end  to  end  would  extend  how 
many  feet  ?  how  many  yards  ? 

Twelve  two-cent  pieces  are  how  much  money  ?  Twelve 
two-cent  rolls  of  lozenges  will  cost  how  much  money  ? 

Express  :  Twelve  twos  are  twenty-four. 

Who  has  a  story  for  twelve  twos? 

Express : 

Once  two.  Five  twos.  Nine  twos. 

Two  twos.  Six  twos.  Ten  twos. 

Three  twos.  Seven  twos.  Eleven  twos. 

Four  twos.  Eight  twos.  Twelve  twos. 


342  FIRST  STEPS   IN   NUMBER. 

We  call  this  the  Tahle  of  Twos, 

Read  the  table  of  twos. 

How  many  gills  in  a  pint  ?  in  two  pints  ?  in  three  pints  ? 
in  four  pints  ?  in  five  pints  ?  in  six  pints  ? 

How  many  quarts  in  a  gallon  ?  in  three  gallons  ?  in  five 
gallons  ?  in  six  gallons  ? 

Write :  4  gills     —  1  pint. 

2  pints    =  1  quart. 
4  quarts  =  1  gallon. 

This  is  the  Tahle  of  Liquid  Measure. 

Read  the  Table  of  Liquid  Measure. 

How  many  things  are  in  a  dozen  ?  in  half  a  dozen  ?  in  a 
dozen  and  a  half?  in  two  dozen? 

Two  dozen  eggs  are  how  many  eggs  ?  Two  dozen  apples 
are  how  many  apples  ? 

Express  :  Two  twelves  are  twenty-four. 

How  many  months  in  a  year  ? 

How  many  months  in  two  years  ? 

How  many  months  in  a  year  and  a  half? 

How  many  sheets  of  paper  in  a  quire  of  paper  ?  In  half 
a  quire  ? 

Express  :  One-half  of  twenty-four  is  twelve. 

How  many  hours  in  a  day  ? 

How  many  hours  in  half  a  day  ? 

How  many  inches  equal  a  foot  ? 

How  many  inches  in  two  feet? 

If  velvet  is  twenty-four  inches  wide,  what  is  half  its 
width  ?     How  many  feet  wide  is  the  velvet  ? 

Twenty-four  oranges  are  how  many  dozen  oranges? 

Twenty-four  months  are  how  many  years  ? 

Express :  Twenty-four  divided  by  twelve  are  two. 

How  many  feet  in  a  yard?  in  three  yards?  in  five 
yards?  in  six  yards?  in  seven  yards?  in  eight  yards? 


THE   NUMBER  TWENTY-FIVE.  343 

How  many  strips  of  carpeting  a  yard  wide  will  be  re- 
quired to  go  across  a  room  twenty-four  feet  long  ? 

How  many  working  days  in  a  week  ?  in  two  weeks  ?  in 
three  weeks  ?  in  four  weeks  ? 

A  man  picking  up  apples  takes  up  a  dozen  at  once. 
When  he  has  picked  up  twenty-four  apples,  how  many 
handfuls  has  he  picked  up  ? 

The  hour-hand  goes  half  way  round  the  clock  every  six 
hours.  How  many  times  does  it  go  half  way  round  the 
clock  in  twenty-four  hours  ? 

How  many  gills  in  a  quart?  in  two  quarts?  in  three 
quarts  ? 

If  I  have  three  quarts  of  jelly,  how  many  glasses,  each 
holding  a  gill,  can  I  fill? 

If  it  takes  five  bottles  of  wine  to  make  a  gallon  of  wine, 
how  many  bottles  will  it  take  to  make  five  gallons  of  wine? 

A  five-sided  figure  is  five  inches  on  each  side.  How  many 
inches  is  it  round  the  figure  ? 

If  a  term  of  school  is  ten  weeks,  how  many  school  days 
in  half  the  term  ? 

For  twenty-five  cents,  how  many  bananas  at  five  cents 
apiece  can  I  buy  ? 

Mary  has  ten  cents,  Susie  has  eight  cents,  and  Annie 
has  seven  cents.  If  they  put  their  money  together,  how 
many  bags  of  peanuts  at  five  cents  a  bag  can  they  buy  ? 

If  five  yards  of  cambric  cost  twenty-five  cents,  what  does 
one  yard  cost  ? 

A  man  caught  twenty-five  fish.  His  little  boy  caught 
a  fifth  as  many  fish.     How  many  did  the  boy  catch  ? 

A  train  of  cars  runs  twenty-five  miles  an  hour.  A  man 
walks  one-fifth  as  far.  How  many  miles  does  the  man  go 
in  an  hour? 


CHAPTER  XXV. 

THE  NUMBER   TWENTY-SEVEN. 


§  47.     The  Number  Twenty-Seven. 

Four  and  three  are  how  many  ? 

Fourteen  and  three  are  how  many  ? 

Twenty-four  and  three  are  how  many  ? 

Eight  threes  and  what  number  make  twenty-seven? 
Then  nine  threes  make  what  number? 

Express:  Nine  threes  are  twenty-seven. 

Nine  three-cent  pieces  are  how  much  money  ? 

Nine  three-cent  pencils  cost  how  much  ? 

Nine  triangles  have  how  many  sides  ? 

Nine  yards  of  chain  are  how  many  feet  of  chain  ? 

Johnny  is  three  years  old.  His  papa  is  nine  times  as 
old.     How  old  is  his  papa  ? 

Here  are  twenty-seven  short  sticks.  How  many  separate 
triangles  can  you  form  with  them  ? 

A  chair-maker  put  three  bars  across  the  back  of  each 
chair.    How  many  chairs  would  twenty-seven  bars  supply  ? 

Twenty-seven  feet  of  rope  are  how  many  yards  of  rope  ? 

In  each  season  there  are  three  months.  How  many  sea- 
sons are  there  in  twenty-seven  months? 

A  man  who  worked  on  a  farm  received  three  dollars 
a  week.  How  many  weeks  did  he  work  to  earn  twenty- 
seven  dollars? 

Express :  Twenty-seven  divided  by  three  are  nine. 


THE   NUMBER  TWENTY-SEVEN.  345 

Which  is  more,  nine  threes  br  three  nines? 

If,  then,  nine  threes  are  twenty-seven,  how  much  are 
three  nines? 

If  there  are  nine  school-months  in  a  year,  how  many 
school-months  in  three  years  ? 

Three  pounds  of  beef  at  nine  cents  a  pound  will  cost 
how  much? 

Three  yards  of  cambric  at  nine  cents  a  yard  will  cost 
how  much  ? 

I  can  buy  crackers  at  nine  cents  a  dozen.  How  many 
dozen  can  I  buy  for  twenty-seven  cents  ? 

How  many  quires  of  paper  at  nine  cents  a  quire  can  I 
buy  for  twenty-seven  cents  ? 

What  part  of  twenty-seven  is  nine  ? 

If  I  divide  twenty-seven  plums  equally  among  three 
children,  how  many  plums  shall  I  give  to  each  ? 

If  three  pounds  of  dates  cost  twenty-seven  cents,  what 
does  one  pound  cost  ? 

If  it  takes  a  man  twenty-seven  days  to  lay  a  certain 
amount  of  pipe,  how  long  will  it  take  him  to  lay  one-third 
as  much  pipe  ? 

If  it  takes  one  man  twenty-seven  days  to  do  a  piece  of 
work,  how  long  will  it  take  three  men? 

Read,  and  give  the  answers: 


9x    3  = 

3x 

=  27 

X    9  =  27 

27-^    3  = 

9x 

=  27 

H-   9=   3 

3x    9  = 

27^ 

=   3 

X    3  =  27 

27-^    9  = 

27^ 

=   9 

+•   3=   9 

J  of  27  = 

18  + 

=  27 

+   9  =  27 

24+    3  = 

3  + 

=  27 

+  24  =  27 

3        9          18 

27 

27 

27 

27          27 

9        3+9 

-9 

-3      - 

-10 

-20         -7 

346  FIRST  STEPS   IN  NUMBER. 


Exercise  for  Review. 


How  many  in  a  half-dozen  ?  How  many  in  two  half- 
dozens  ?     Which  is  more,  two  half-dozens  or  one  dozen  ? 

How  many  months  in  half  a  year  ?  How  many  months 
in  two  halves  of  a  year?  Which  is  the  longer  time,  two 
halves  of  a  year  or  a  whole  year  ? 

How  many  sheets  of  paper  in  half  a  quire  ?  In  two 
halves  of  a  quire  ?    Which  is  more,  two  halves  or  a  whole  ? 

How  many  halves  in  a  whole  ? 

How  many  inches  in  a  third  of  a  foot?  How  many 
inches  in  three-thirds  of  a  foot  ? 

How  many  eggs  in  a  third  of  a  dozen  ?  In  three-thirds 
of  a  dozen  ?  Which  is  more,  three-thirds  of  a  dozen  or  a 
whole  dozen  ? 

How  many  hours  in  a  third  of  a  day  ?  In  three-thirds 
of  a  day  ?  Which  is  the  longer  time,  three-thirds  of  a  day 
or  a  whole  day  ? 

How  many  thirds  in  a  whole  ? 

How  many  sheets  of  paper  in  a  fourth  of  a  quire  ?  In 
four-fourths  of  a  quire  ?  Which  is  more,  four-fourths  of  a 
quire  or  a  whole  quire  ? 

How  many  months  in  a  fourth  of  a  year?  In  four- 
fourths  of  a  year  ?  Which  is  longer,  four- fourths  of  a  year 
or  a  whole  year  ? 

How  many  fourths  in  a  whole  ? 

Express  :  One-half  of  twelve  is  six. 

One-third  of  twelve  is  four. 
One-fourth  of  twelve  is  three. 
One-sixth  of  twelve  is  two. 

Which  is  most,  one-half,  one-third,  one-fourth,  or  one- 
sixth  of  twelve  ?  Which  is  least,  one-half,  one-third,  one 
fourth,  or  one-sixth  of  twelve  ?  Which  is  more,  one-third 
or  one-fourth  of  twelve  ? 


THE  NUMBER   TWENTY-SEVEN.  347 

Express  :  One-half  of  twenty-four  is  twelve. 
One-third  of  twenty-four  is  eight. 
One-fourth  of  twenty-four  is  six. 
One-sixth  of  twenty-four  is  four. 
One-eighth  of  twenty-four  is  three. 

Which  is  most,  one-half,  one-third,  one-fourth,  one-sixth, 
or  one-eighth  of  twenty-four?  Which  is  least,  one-half, 
one-third,  one-fourth,  one-sixth,  or  one-eighth  of  twenty- 
four  ?  Which  is  more,  one-third  or  one-sixth  of  twenty- 
four  ? 

Which  is  more,  one-half  of  sixteen  or  one-eighth  of  six- 
teen ?  One-half  of  eighteen  or  one-sixth  of  eighteen  ?  One- 
third  of  eighteen  or  one-sixth  of  eighteen  ? 

Which  is  more,  one-half  of  anything  or  one-third  of  the 
same  thing?  One-half  or  one-fourth?  One-half  or  one- 
sixth  ?  One-half  or  one-eighth  ?  One-third  or  one-fourth  ? 
One-third  or  one-sixth  ?     One-sixth  or  one-eighth  ? 

Here  is  a  large  cube  cut  up  into  eight  small  cubes.  How 
do  the  small  cubes  compare  in  size  ?  (Equal.)  Show  me 
one-half  of  the  cube.  Show  me  one-fourth  of  the  cube. 
How  many  fourths  of  the  cube  can  you  find  in  one-half 
the  cube  ? 

How  many  fourths  of  an  apple  does  it  take  to  equal  one- 
half  of  an  apple?  How  many  fourths  of  an  orange  to 
equal  half  an  orange  ? 

One-half  of  a  dollar  equals  how  many  fourths  of  a  dollar  ? 
One-half  of  a  day  equals  how  many  fourths  of  a  day  ? 

Write  :  One-half  equals  two-fourths.     (-J-  =  f  •) 

Bead  and  give  the  answers  :  — 


i+i=^ 

|-i  =  ^ 

l-i  =  ir 

l  +  i=    ? 

i-i=T 

i+i=  ? 

1-|  =  T 

^f+i=    ? 

i  +  i  =  T 

i-i  =  T 

1-I  =  ir 

i+i=  ? 

f-i  =  T 

i-|  =  T 

1-|  =  T 

i  +  i=    ? 

348  FIRST  STEPS   IN  NUMBER. 

Look  at  this  divided  cube  again.  Into  how  many  small 
cubes  is  it  divided  ?  (Eight.)  How  do  the  small  cubes 
compare  in  size  ?  (Equal.)  Show  me  half  of  the  cube. 
Show  me  one-eighth  of  the  cube.  How  many  eighths  of 
the  cube  can  you  find  in  a  half  of  the  cube  ? 

Here  is  a  circle.  Tell  me  into  what  it  is  divided. 
(Eighths.)  Show  me  one-half  of  the  circle.  Show  me 
one-eighth  of  the  circle.  How  many  eighths  of  the  circle 
can  you  find  in  one-half  of  the  circle  ? 

Here  is  a  square  marked  off  on  the  board.  Into  what 
is  it  divided  by  the  lines  that  I  have  drawn  through  it  ? 
(Eighths.)  Show  me  half  of  the  square.  Show  me  one- 
eighth  of  the  square.  How  many  eighths  of  the  square 
can  you  find  in  half  of  the  square  ? 

One-half  of  a  pie  equals  how  many  eighths  of  the  pie  ? 

One  half  of  a  dollar  equals  how  many  eighths  of  a  dollar  ? 

Write  :  One-half  equals  four-eighths. 

Copy  and  complete  : 
f  +  l'^Y  i  +  |  — -gr  i  +  f'^-g-  i~i  —  -E 

You  may  take  the  divided  cube  and  find  how  many 
eighths  of  the  cube  there  are  in  a  fourth  of  the  cube. 

Here  is  an  apple  that  is  divided.  Find  how  many 
eighths  of  the  apple  it  takes  to  make  a  fourth  of  the  apple. 

Here  is  a  circle  that  is  divided.  How  many  eighths  of 
the  circle  equal  a  fourth  of  the  circle  ? 

How  many  eighths  of  an  orange  must  you  have  to  equal 
my  fourth  of  an  orange  ? 

How  many  eighths  of  a  mile  equal  one-fourth  of  a  mile  ? 

Write  :  One-fourth  equals  two-eighths. 

Copy  and  complete  :  — 


CHAPTER  XXVI. 

THE   NUMBER  TWENTY-EIGHT. 


§  48.     The  Number  Twenty-Eight. 

Four  and  four  are  how  many? 

Fourteen  and  four  are  how  many  ? 

Twenty -four  and  four  are  how  many  ? 

Six  fours  and  four  are  how  many  ? 

Seven  fours  then  are  how  many  ? 

Seven  chairs  have  how  many  legs  ? 

Seven  wagons  have  how  many  wheels  ? 

If  a  cask  holds  seven  gallons,  how  many  quarts  does  it 
hold? 

If  a  pail  holds  seven  pints,  how  many  gills  does  it  hold  ? 

A  sheet  of  note  paper  has  four  pages.  Seven  sheets  of 
note  paper  have  how  many  pages  ? 

If  there  are  four  panes  of  glass  in  one  window,  how  many 
panes  of  glass  are  there  in  seven  windows  ? 

Seven  yokes  of  oxen  have  how  many  horns  ? 

Twenty-eight  horse-shoes  will  shoe  how  many  horses  all 
round? 

Twenty-eight  horses  will  supply  how  many  four-horse 
barges  ? 

How  many  oranges  at  four  cents  apiece  can  be  bought 
for  twenty-eight  cents  ? 

In  twenty-eight  weeks  how  many  moons,  if  there  is  a 
moon  every  four  weeks? 

One  and  seven  are  how  many  ? 


350  TmST  STEPS   IN   NUMBER. 

Eleven  and  seven  are  how  many  ? 

Twenty-one  and  seven  are  how  many  ? 

Three  sevens  and  seven  are  how  many? 

Four  sevens  are  how  many  ? 

In  four  weeks  how  many  days  ? 

Four  quarts  of  peanuts  at  seven  cents  a  quart  will  cost 
how  much  ? 

Give  me  an  example  for  :  Four  sevens  are  twenty-eight. 

There  are  twenty-eight  days  in  the  month  of  February. 
How  many  weeks  are  there  in  February  ? 

If  a  horse  travels  seven  miles  an  hour,  how  many  hours 
will  it  take  him  to  travel  twenty-eight  miles  ? 

Twenty-eight  dollars  will  buy  how  many  pairs  of  boots 
at  seven  dollars  a  pair  ? 

Two  dozen  and  a  third  of  a  dozen  eggs  are  packed  in 
layers  of  seven  each.     How  many  layers  are  there  ? 

A  little  mill-sweeper  earns  seven  cents  every  half-day. 
How  many  days  must  he  work  to  earn  twenty-eight  cents  ? 

What  is  one-fourth  of  twenty-eight  ? 

If  I  have  a  quarter  of  a  dollar  and  a  three-cent  piece, 
and  you  have  a  fourth  as  much  money  as  I,  how  much 
money  have  you  ? 

There  were  twenty-eight  days  in  February.  Three- 
fourths  of  the  days  were  stormy.  How  many  days  were 
stormy  ? 

If  there  are  twenty-eight  slats  in  a  blind,  how  many 
slats  are  there  in  three-fourths  of  the  blind  ? 

In  a  long  ladder  there  were  twenty-eight  rounds,  but  a 
fourth  of  the  rounds  got  broken.  How  many  rounds  were 
there  then  in  the  ladder  ? 

If  I  cut  a  stick  of  wood  which  is  two  feet  and  four  inches 
long  into  sticks  each  seven  inches  long,  how  many  sticks 
shall  I  make  ?     How  many  cuts  shall  I  make  ? 


THE   NUMBER   TWENTY-EIGHT.  351 

What  numbers  shall  I  need  for  these  blanks  ? 


7x    4  = 

21+7  = 

28 -f- 

=   4 

28^   4  = 

14  + 14  = 

28-^ 

=   7 

4x    7  = 

24+   4  = 

4x 

=  28 

28^   7  = 

20+8  = 

7x 

=  28 

J  of  28  = 

18  + 10  = 

14  + 

=  28 

28 

28 

28 

28 

28 

28 

-   7 

-21 

-   4 

-24 

-10 

14 

Exercise  for  Review. 

Count  by  twos  to  twenty-eight. 

Count  by  threes  to  twenty-seven. 

Count  by  fours  to  twenty-eight. 

Count  by  fives  to  twenty-five. 

Count  by  sixes  to  twenty-four. 

Count  by  sevens  to  twenty-eight. 

Count  by  eights  to  twenty-four. 

Count  by  nines  to  twenty-seven. 

Count  by  tens  to  one  hundred. 

How  many  dozen  and  what  part  of  a  dozen  bananas  are 
there  in  a  bunch  of  twenty-eight  bananas  ? 

How  many  score  and  how  many  more  chickens  have  I,  if 
I  have  twenty-eight  chickens  ? 

How  many  quarts  and  what  part  of  a  quart  of  jelly  in 
twenty-eight  gills? 

How  many  gallons  of  oil  in  a  tank  containing  twenty- 
eight  quarts? 

How  many  years  and  what  part  of  a  year  in  twenty- 
eight  months  ? 

How  many  days  and  what  part  of  a  day  in  twenty-eight 
hours  ? 


352  FIRST  STEPS  IN   NUMBER. 

How  many  yards  and  how  many  feet  besides  in  twenty- 
eiglit  feet  of  rope  ? 

Twenty-eight  cents  will  buy  how  many  two-cent  postage 
stamps?  How  many  three-cent  pencils  and  what  will 
remain  ?  How  many  yards  of  curtain-cord  at  four  cents  a 
yard?  How  many  dozen  peaches  at  five  cents  a  dozen, 
and  what  will  remain  ?  How  many  quires  of  paper  at  six 
cents  a  quire,  and  what  will  remain  ?  How  many  cakes 
of  maple  sugar  at  seven  cents  a  cake  ?  How  many  quarts 
of  blueberries  at  eight  cents  a  quart,  and  what  will  remain  ? 
How  many  pounds  of  crackers  at  nine  cents  a  pound,  and 
what  will  remain  ?  How  many  loaves  of  bread  at  ten  cents 
a  loaf,  and  what  will  remain  ?  How  many  dozen  pens  at 
eleven  cents  a  dozen,  and  what  will  remain? 

If  a  boy  works  every  day  in  the  week  and  earns  a  half- 
dollar  a  day,  how  many  weeks  must  he  work  to  earn 
twenty-seven  dollars? 

If  I  pay  ten  cents  for  a  bottle  of  ink  which  holds  a  gill, 
and  fifty  cents  for  a  quart  bottle  of  ink,  how  much  do  I 
save  in  buying  ink  by  the  quart? 

If  you  sleep  one-third  of  the  day  and  I  sleep  one-fourth 
of  the  day,  who  sleeps  the  more  hours  ?  How  many  more 
hours  ? 

If  John  eats  a  half-dozen  peaches  and  Mary  eats  a  quarter 
of  a  dozen,  who  eats  the  more  peaches  ?     How  many  more  ? 

If  I  write  a  third  of  the  day  to-day,  and  a  sixth  of  the 
day  to-morrow,  how  many  more  hours  shall  I  write  to-day 
than  to-morrow  ? 

Which  is  the  larger  part,  a  half  of  an  apple  or  a  third  of 
the  same  apple  ?  A  half  of  a  stick  of  candy  or  a  third  of 
the  same  stick  of  candy  ? 

Into  how  many  parts  will  you  divide  anything  to  divide 
it  into  halves  ?  to  divide  it  into  thirds  ?  to  divide  it  into 
fourths  ?  to  divide  it  into  fifths  ?  into  sixths  ?  into  eighths  ? 


CHAPTER   XXVII. 

THE    NUMBER    THIRTY. 


§  49.   The  Number  Thirty. 

Twenty-five  and  five  are  how  many  ? 

Five  fives  and  five  are  how  many  ? 

Six  fives  are  how  many  ? 

Six  bunches  of  envelopes  at  five  cents  a  bunch  will  cost 
how  much? 

If  you  have  five  cents  and  I  have  six  times  as  much,  how 
much  money  do  I  have? 

Annie  is  five  years  old  and  her  mamma  is  six  times  as 
old.     How  old  is  her  mamma? 

Thirty  cents  will  buy  how  many  bananas  at  five  cents 
apiece  ? 

In  thirty  school-days  how  many  weeks  of  school? 

A  garden  is  thirty  feet  long  and  five  feet  broad;  how 
many  times  its  breadth  is  its  length? 

Nellie's  little  reading-book  has  thirty  pages.  If  she 
reads  five  pages  a  week,  in  how  many  weeks  will  she  finish 
the  reader  ? 

What  is  one  of  the  six  equal  numbers  into  which  thirty 
can  be  divided  ?    What  number  then  is  one-sixth  of  thirty  ? 

What  piece  of  money  is  one-sixth  of  thirty  cents?   . 

If  six  bottles  of  ink  cost  thirty  cents,  what  does  one  bot- 
tle cost? 

If  six  spools  of  thread  cost  thirty  cents,  what  does  one 
spool  cost? 


354  FIRST   STEPS    IN   NUMBER. 

James  found  five  eggs  early  in  the  morning;  but  that 
was  only  one-sixth  of  the  number  he  found  before  night. 
How  many  did  he  find  in  all  ? 

Express :    ,  Six  fives  are  thirty. 

Thirty  divided  by  fiye  are  six. 
One-sixth  of  thirty  is  ^ye. 

Twenty-four  and  six  are  how  many  ? 

Twenty-four  and  six  are  how  many  sixes? 

How  many  working  days  in  five  weeks? 

How  many  balloons  has  a  man  who  has  five  bunches 
with  half  a  dozen  in  each  bunch  ? 

A  ship  that  makes  a  voyage  every  six  months  will  make 
how  many  voyages  in  thirty  months  ? 

A  boy  who  earns  a  cent  a  day  must  work  how  many 
■  weeks  to  earn  thirty  cents  ? 

A  boy  who  earns  six  dollars  a  month  must  work  how 
many  months  to  earn  thirty  dollars  ? 

What  is  one  of  the  five  equal  numbers  which  make 
thirty  ? 

What  is  one-fifth  of  thirty  ? 

What  two  equal  pieces  of  money  make  one-fifth  of  thirty  ( 

One-fifth  of  thirty  months  is  what  part  of  a  year? 

One-fifth  of  thirty  eggs  is  what  part  of  a  dozen  eggs  ? 

One-fourth  of  a  quire  of  paper  is  what  part  of  thirty 
sheets  of  paper  ? 

One-half  a  foot  is  what  part  of  thirty  inches  ? 

Read  and  give  the  answers : 

i^of30-=  X    5-30  30-^  =10 

I  of  30=  X    3  =  30  30^  =    3 

I  of  30=  X    6  =  30  30-^  =   6 

30  -^  10  =  X  10  =  30  30  -f-  =    5 

30--    6=  V  of  30  =  10  30-^  =15 


THE   NUMBER   THIRTY.  355 

30-^   5=-  of  30--   6  30—  =20 

3  X  10  =  of  30  =   5  30  —  =  15 

5x    6=  of30=15  30-  =24 

6x5=  +6  =  30  30 -=25 

30           30  30               30  30  30 

2              3  —10           -15  -20  +40 


Exercise    for    Review. 

When  anything  is  divided  into  five  equal  parts,  what  is 
each  part  called  ?     What  are  four  of  the  parts  called  ? 

When  anything  is  divided  into  seven  equal  parts,  what 
is  each  part  of  the  whole  ?  What  part  of  the  whole  are 
three  parts  ?  four  parts  ?  seven  parts  ? 

What  do  you  mean  by  one-eighth  of  anything  ?  by  three- 
eighths  of  anything?  by  two-fifths  of  anything?  by  five 
fifths  of  anything  ?  by  one-sixth  of  anything  ? 

I  have  a  half  a  dollar  and  Annie  has  a  quarter  of  a  dol- 
lar. Which  has  the  more  money  ?  How  much  more  money 
have  I  than  Annie  ? 

How  many  quarters  of  a  dollar  does  it  take  to  equal  half 
a  dollar? 

I  am  in  school  a  quarter  of  the  day.  Sadie  is  in  school 
only  one-eighth  of  the  day.  How  many  times  as  many 
hours  am  I  in  school  as  Sadie? 

There  are  sixteen  ounces  in  a  pound.  I  have  here  two 
weights.  One  is  one-fourth  of  a  pound,  the  other  is  one- 
eighth  of  a  pound.  How  many  times  as  heavy  is  one  as 
the  other? 

I  have  here  a  half-pound  weight.  How  many  eighth- 
pound  weights  will  it  take  to  balance  the  half-pound  weight  ? 

One-half  of  a  pound  of  candy  will  make  how  many  pack- 
ages of  candy  each  weighing  an  eighth  of  a  pound  ? 


356  FIRST  STEPS   IN   NUMBER. 

How  many  blocks  of  chocolate,  each  weighing  an  eighth 
of  a  pound,  must  you  put  together  to  make  a  half  a  pound 
of  chocolate  ?  to  make  a  quarter  of  a  pound  of  chocolate  ? 

In  our  climate  snow  is  on  the  ground  a  third  of  the 
year,  and  only  a  sixth  of  the  year  is  warm  summer  weather. 
How  many  times  as  much  winter  as  summer  have  we  ? 

Each  loaf  of  ginger-bread  takes  a  sixth  of  a  dozen  eggs. 
How  many  loaves  of  ginger-bread  can  be  made  from  a  third 
of  a  dozen  eggs  ? 

How  many  sixths  of  an  apple  does  it  take  to  equal  a 
third  of  an  apple  ? 

A  third  of  a  yard  will  make  how  many  sixths  of  a  yard  ? 

It  snowed  four  hours  to-day ;  what  part  of  the  day  has 
it  snowed  ?  If  it  had  snowed  twice  as  many  hours  of  the 
day,  what  part  of  the  day  would  it  have  snowed  ? 

Nellie  ate  a  third  of  a  pound  of  dates.  If  I  ate  half  the 
quantity  she  ate,  what  part  of  a  pound  did  I  eat  ? 

If  a  third  of  a  pound  of  maple  sugar  costs  six  cents,  what 
will  a  sixth  of  a  pound  cost?  what  will  a  half  a  pound  cost? 

Take  this  number- work: 


i=^ 

i+i=T 

i-i  =  T 

i+i  =  ? 

i  =  T 

i  +  i  =  T 

i-i  =  T 

i+i  =  T 

i=a 

i+i=Tr 

i-i  =  F 

l+i  =  ^ 

i  =  T 

\  +  \  =  T 

i-i  =  T 

1+1=  ? 

i  =  ir 

i  +  i  =  F 

i-i  =  Tr 

f+f=? 

What  will  five  pairs  of  boots  cost  at  five  dollars  a  pair  ? 

On  Mamie's  fifth  birthday  she  invited  five  children  to 
visit  her;  each  child  invited  was  five  years  old.  What 
was  the  sum  of  the  little  folks'  ages,  counting  in  Mamie  ? 

In  a  caravan  there  were  four  rows  of  camels  and  five 
camels  in  each  row.    How  many  camels  were  in  the  caravan? 


THE   NUMBER  THIRTY.  357 

A  boy  received  three  five-cent  pieces  for  shovelling  the 
snow  from  a  sidewalk.     How  much  money  did  he  receive  ? 

Count  by  fives  as  far  as  you  can. 

How  many  fives  make  thirty?  make  fifteen?  make 
twenty-five?   make  twenty? 

Count  by  threes  to  thirty. 

How  many  threes  make  twelve  ?  make  eighteen  ?  make 
twenty-four?  make  fifteen?  make  thirty?  make  twenty- 
one? 

Twenty  gills  of  milk  will  cost  how  much  at  four  cents 
a  pint  ? 

Twenty-four  quarts  of  wine  will  cost  how  much  at  four 
dollars  a  gallon  ? 

In  sixteen  weeks  how  many  new  moons,  if  there  is  a  new 
moon  every  four  weeks? 

If  I  have  twenty-eight  quarters  of  dollars,  how  many 
dollars  have  I  ? 

Five  fours  are  how  many  ?  three  fours  ?  six  fours  ?  four 
fours?  seven  fours? 

Count  by  fours  to  twenty-eight. 

How  many  faces  have  two  cubes  ? 

How  many  sides  have  three  boxes  ? 

How  many  sides  has  a  room,  counting  the  floor  and  the 
ceiling  ?     How  many  sides  have  four  rooms  ? 

In  five  half-years  how  many  months  ? 

Count  by  sixes  to  thirty. 

Three  cubes  have  how  many  corners  ? 

Two  pounds  of  candy  will  fill  how  many  little  bags,  if 
there  is  an  eighth  of  a  pound  in  each  bag  ? 

Count  by  eights  to  twenty-four. 

In  a  month  of  twenty-eight  days  how  many  weeks  ? 

There  are  seven  colors  in  a  rainbow.  If  three  rainbows 
were  placed  side  by  side,  how  many  strips  of  color  would 
there  be  ?    How  many  colors  ? 


358  FIRST  STEPS  IN   NUMBER. 

Count  by  sevens  to  twenty- eight. 

Nine  inches  are  a  quarter  of  a  yard.  A  half  a  yard 
then  is  how  many  inches  ?  Three-quarters  of  a  yard  are 
how  many  inches  ? 

Count  by  nines  to  twenty-seven. 

Count  by  tens  as  far  as  you  can. 

Count  by  elevens  as  far  as  you  can. 

Two  dozen  oranges  are  how  many  oranges? 

Two  feet  are  how  many  inches? 

In  two  years  how  many  months  ? 

Two  cubes  have  how  many  edges? 

One-half  of  a  pint  is  how  many  gills  ? 

One-half  a  working  week  is  how  many  days  ? 

One-half  of  an  apple  is  how  many  eighths  of  an  apple  ? 

One-half  of  a  dime  is  how  many  cents  ? 

One-half  of  a  foot  is  how  many  inches? 

One-half  of  fourteen  days  is  how  many  weeks  ? 

One-half  of  a  pound  is  how  many  ounces,  if  there  are 
sixteen  ounces  in  a  pound  ? 

There  are  eighteen  inches  in  half  a  yard.  If  this  ruler 
is  half  a  yard  long,  how  long  is  half  the  ruler  ? 

One-half  of  a  score  of  persons  is  how  many  persons  ? 

One-half  of  twenty-two  bonnets  is  how  many  bonnets? 

One-half  of  a  day  is  how  many  hours  ? 

One-half  of  February  is  how  many  days  ? 

One-half  of  a  month  which  has  thirty  days  is  how  many 
days  ? 

One-half  of  fifty  cents  is  how  many  cents? 

One-third  of  a  year  is  how  many  months?  .One-fourth 
of  a  year  ?     One-sixth  of  a  year  ? 

One-third  of  a  day  is  how  many  hours  ?  One-fourth  of 
a  day  ?     One-sixth  of  a  day  ?     One-eighth  of  a  day  ? 

One-fourth  of  a  score  is  how  many?  One-fifth  of  a 
score  ? 


THE   NUMBER   THIRTY.  359 

One-fifth  of  a  quarter  of  a  dollar  is  how  much  ? 

One-fifth  of  a  month  is  how  many  days  ? 

Divide  seven  by  four  and  tell  me  the  answer.  Divide 
nine  by  five.  Divide  sixteen  by  three ;  eighteen  by  four ; 
twenty-one  by  ten  ;  twenty-four  by  nine. 

Take  this  number  work  : 


3x    7  = 

8x    3  = 

iof30  = 

iof30  = 

7x    3  = 

6x    4  = 

3x    9  = 

|of30  = 

21-^   3  = 

24  H-   6  = 

27-^    3  = 

|of30  = 

21^   7  = 

24-^   8  = 

iof27  = 

|of30  = 

iof21  = 

5x    5  = 

4x    7  = 

6x    5  = 

2x11  = 

iof25  = 

28^   4  = 

80-^   6  = 

12  X    2  = 

iof20  = 

iof28  = 

30^   5  = 

Name  the  sum  of  each  couple  of  numbers  as  I  point. 
7  4  8  5  9  3  11  4  8  8  7 
68564      10       37765 

See  if  you  can  add  by  couples  of  numbers  when  there 

are  several  numbers  to  be  added,  as  in  this  case  :  3 

When  I  point  to  5,  think  of  the  sum  of  2  and  5,  or     4 

7.  When  I  point  to  6,  think  of  the  sum  of  2  and  6,  or     5 

8,  and  say,  "  7  and  8  are  15."  When  I  point  to  5,  say,  4 
"And  9  are  24."  When  I  point  to  3,  say,  ''And  7  are  6 
31."  2 

When  I  point  this  time,  try  if  you  can  add  quickly     5 
by  the  couples  of  numbers,  thus :  7,  15,  24,  31.  2 

Add  these  numbers  in  the  same  way : 

25  6  2  10  6567 
724543563 
362438755 
5110    5    4   10   737 


360  FIRST   STEPS   IN   NUMBER. 

United  States  Money. 

I  have  two  dollars  in  my  purse.  Who  will  express  on 
the  board  what  I  have  in  my  purse?  (2  dollars.)  You 
are  right,  but  I  can  express  it  in  another  way :  $2. 

Express:  Three  dollars.  Seven  dollars.  Five  dollars. 
Twenty  dollars.  Twenty-five  dollars.  Eight  dollars.  One 
hundred  dollars.  Sixty  dollars.  Forty-seven  dollars. 
Eighty-six  dollars. 

Read  what  you  have  expressed. 

What  have  I  expressed?  ($5.)  I  wish  to  express  five 
dollars  and  twenty-five  cents.  Can  you  show  me  how? 
Ned  has  it  right.  We  always  put  the  dot  between  the 
dollars  and  cents  so  the  cents  shall  not  get  into  dollars' 
place.  The  dollars  are  in  the  highest  class,  and  the  little 
cents  don't  belong  with  them. 

Read  what  I  have  expressed : 

$6.25        $7.84        $9.63        $12.44        $73.82 
$3.50        $2.04        $8.02        $75.08        $60.10 

Express:  Three  dollars  and  twenty-six  cents. 
Eight  dollars  and  sixty  cents. 
Twelve  dollars  and  a  half. 
Sixteen  dollars  and  a  quarter. 
Thirty  dollars  and  ten  cents. 
Three  dollars  and  five  cents. 
Five  dollars  and  three  cents. 
Twenty  dollars  and  two  cents. 
Thirty  dollars  and  three  cents. 
Fifty  dollars  and  five  cents. 

Dry  Measures. 

Who  has  seen  wooden  measures  like  these  somewhere 
else  ?  What  have  you  seen  measured  in  any  one  of  them  ? 
How  much  does  the  smallest  measure  hold  ?     How  much 


THE   NUMBER  THIRTY.  361 

does  the  next  larger  one  hold  ?     How  many  times  as  much 
as  the  first  measure  will  the  quart  measure  hold  ? 

Who  knows  what  the  largest  measure  is  called  ?  It  is  a 
jpeclc  measure.  If  you  buy  this  largest  measure  full  of 
beans,  what  quantity  will  you  buy?  Name  some  articles 
that  are  sold  by  the  peck. 

I  have  here  some  beans.  Who  would  like  to  find  how 
many  quarts  of  beans  the  peck  measure  holds?  Willie 
may  measure,  and  Annie  may  put  a  mark  on  the  board  for 
every  quart  he  puts  into  the  peck  measure. 

How  many  quarts  does  it  take  to  make  a  peck  ? 

If  a  horse  eats  a  half  of  a  peck  of  oats  at  a  meal,  how 
many  quarts  of  oats  does  he  eat  ? 

If  I  pick  a  peck  and  a  half  of  blueberries,  how  many 
quarts  of  blueberries  do  I  pick  ? 

If  you  buy  two  pecks  of  oats,  how  many  quarts  of  oats 
do  you  buy? 

A  party  of  boys  went  chestnutting  and  found  two  pecks 
and  a  half.     How  many  quarts  of  chestnuts  did  they  find  ? 

In  three  pecks  how  many  quarts  ? 

If  the  peck  measure  is  a  quarter  full,  how  many  more 
quarts  will  it  hold  ?  If  it  is  three-quarfcers  full,  how  many 
more  quarts  will  it  hold  ? 

If  the  peck  measure  is  five-eighths  full,  how  many  quarts 
are  in  the  measure  ? 

Express :  Two  pints  are  one  quart. 
Eight  quarts  are  one  peck. 


In  what  two  ways  can  you  express  on  the  board  the 
addition  of  twenty  and  thirty  ? 

In  what  two  ways  can  you  express  the  subtraction  of 
twenty  from  thirty  ? 

In  what  two  ways  can  you  express  two  times  thirty? 


362  FIRST  STEPS   IN    NUMBER. 

In  what  one  way  can  you  express  thirty  divided  by  six  ? 
We  have  another  way  for  this :  6)30 

5 
You  may  express  in  this  new  way : 

Thirty  divided  by  six. 

Twenty  divided  by  five. 

Twenty-seven  divided  by  nine. 

Twenty-eight  divided  by  seven. 

Twenty-eight  divided  by  four. 

Twenty-five  divided  by  ^ye. 

Twenty-four  divided  by  six. 

Twenty-four  divided  by  eight. 

Twenty-one  divided  by  seven. 
Pead  what  you  have  expressed. 

Take  this  number  work : 

4)16  5)30  4)28  12)24 

6)18  7)28  6)24  11)22 

7}2i  8)24  8}27  10)50 


CHAPTER  XXVIII. 

FIRST  STEPS  IN  WRITTEN  ARITHMETIC. 


§  50.     Addition. 

When  the  sum  of  the  units  does  not  exceed  nine. 

Three  men  pastured  their  sheep  in  the  same  lot.  One 
man  had  thirteen  sheep  in  the  lot,  another  had  twenty- 
one,  and  the  other  had  thirty-four.  I  want  you  to  find 
how  many  sheep  were  in  the  lot.  Show  me  with  the 
splints  the  number  thirteen  ;  below  it  put  twenty-one,  and 
below  the  other  two  numbers  put  thirty -four.  In  thirteen 
how  many  ones  besides  the  one  ten  ?  In  twenty-one  how 
many  besides  the  two  tens?  In  thirty-four  how  many 
ones  besides  the  three  tens  ?  How  many  ones  altogether  ? 
(8.)  How  many  tens  in  thirteen?  in  twenty-one?  in 
thirty-four?  How  many  tens  altogether?  Six  tens  ami 
eight  are  how  many  ?  Then  how  many  sheep  were  in  the 
pasture  ? 

Note.  Let  the  numbers  be  shown  in  tens  and  ones,  the  tens  being 
each  in  a  bundle  by  itself. 

Let  examples  be  done  in  this  way  until  the  children  can  perform 
the  operations  in  the  right  order  without  any  suggestions  from  the 
teacher.  When  they  can  do  this,  they  are  ready  to  transfer  their 
work  to  the  board. 

Who  can  express  this  example  on  the  board?  Willie 
may  express  it.     All  may  express  it. 

Who  would  like  to  try  one  at  the  board  and  not  use  the 
splints?  Those  who  cannot  find  the  answer  on  the  board 
may  use  the  splints. 


364 


FIRST  STEPS   IN   NUMBER. 


Take  this  example :  A  merchant  had  three  pieces  of 
cloth.  In  one  piece  were  fifteen  yards,  in  another  thirty- 
one,  and  in  the  other  twenty- three.  How  many  yards  of 
cloth  in  the  three  pieces  ? 

Take  this :  I  spent  fourteen  cents  for  some  sugar,  forty- 
two  cents  for  some  tea,  and  thirty  cents  for  some  butter. 
How  many  cents  did  I  spend  ? 

Take  this :  How  many  hours  in  a  day  and  a  half  and 
ten  hours  more  ? 

Find  the  sum  of  twelve,  thirteen,  fourteen,  and  fifty. 

Find  the  sum  of  twenty-three,  twenty,  thirty-three,  and 
thirteen. 

Find  the  sum  of  forty-two,  twenty-one,  fourteen,  and 
twenty -two. 


Find  tte 

sum: 

32 

43 

33 

25 

31 

60 

21 

13 

22 

30 

40 

19 

23 

10 

11 

10 

18 

10 

12 

11 

12 

13 

10 

30 

10 

20 

21 

11 

20 

20 

43 

61 

37 

55 

72 

91 

25 

33 

40 

31 

81 

20 

31 

42 

51 

60 

90 

65 

50 

20 

30 

81 

63 

73 

70 

71 

20 

70 

51 

50 

§  51.   Subtraction. 

When  the  number  in  each  order  of  the  minuend  is  greater 
than  the  corresponding  number  in  the  subtrahend. 

I  had  fifty-seven  chickens  and  sold  twenty-four.     I  want 
you  to  find  how  many  chickens  I  had  left.     Show  me  with 


FIRST  STEPS   IN  WRITTEN   ARITHMETIC.  355 

the  splints  the  number  I  had  before  I  sold  any.  Take  out 
the  ones  I  sold.  Take  out  the  tens  I  sold.  How  many 
did  I  have  left  ? 

Note.  Let  the  pupils  solve  many  similar  problems,  .and  always 
insist  that  the  difference  between  the  ones  be  found  first.  When  the 
answer  to  any  example  of  this  kind  can  be  readily  determined 
through  the  use  of  objects,  let  the  examples  be  performed  at  the 
board. 

Express  this  example  on  the  board :  A  man  made  a 
journey  of  sixty-eight  miles  on  horseback.  When  he  had 
gone  forty-five  miles,  how  much  farther  had  he  to  go  ? 

What  number  will  you  subtract  first?  What  next? 
What  is  the  answer  ? 

Express  these  examples  and  find  the  answers : 

A  train  of  cars  is  seventy-nine  minutes  going  from  one 
station  to  another.  If  the  train  is  in  motion  only  sixty- 
seven  minutes,  how  much  time  is  taken  in  making  stops  ? 

A  man  who  had  ninety-six  acres  in  his  farm  sold  twenty- 
one  acres.     How  many  acres  did  his  farm  then  contain. 

There  were  forty-seven  trees  in  an  orchard,  but  fourteen 
were  cut  down.     How  many  remained  standing? 

Find  the  difference  between  seventy-eight  and  thirty- 
five. 

Find  the  difference  between  eighty-nine  and  fifty-four. 

Find  the  difference  between  ninety-nine  and  sixty-six. 

Find  the  difference  between  eighty-seven  and  thirty- 
three. 

Find  the  difference : 

98  87  75  69  58  87 

-43        -34        -32        -25        -15        -53 


99 

88 

77 

97 

89 

86 

-65 

-53 

-34 

-62 

-66 

-22 

366  FIEST  STEPS  IN  NUMBER. 

§  52.   Multiplication. 

When  the  multiplier  is  less  than  ten,  and  the  product  of 
any  order  in  the  multiplicand  (unless  it  be  the  highest)  is 
less  than  ten. 

It  takes  twenty-one  buttons  for  one  jacket.  I  want  to 
find  how  many  buttons  it  will  take  for  four  jackets ;  you 
may  help  me.  Show  me  first  how  many  ones  are  required 
for  four  jackets,  since  it  takes  one  for  each  jacket.  Show 
me  next  how  many  tens  are  required  for  four  jackets,  since 
it  takes  two  tens  for  each  jacket.  How  many  buttons  in 
all? 

There  were  two  dozen  buttons  on  each  card ;  I  want  you 
to  find  how  many  there  were  on  two  cards.  First  show 
how  many  ones  on  the  two  cards,  since  there  were  four  on 
each  card.  Next  show  how  many  tens  on  two  cards,  since 
there  were  two  tens  on  each  card.  How  many  buttons  on 
both  cards  ? 

If  I  have  two  quires  of  paper,  how  many  sheets  of  paper 
do  I  have. 

How  many  days  are  there  in  four  months  of  thirty-one 
days  each  ? 

There  are  thirty-two  quarts  in  a  bushel.  How  many 
quarts  in  four  bushels  ? 

If  you  go  to  school  twenty-one  days  in  a  month,  how 
many  days  do  you  go  in  nine  months  ? 

[Give  similar  examples,  and  let  the  product  be  found  with  the 
objects  until  the  pupils  can  do  the  work  readily.  Always  require 
the  product  of  the  ones  found  first.  Pass  to  board  work  when  the 
objects  are  no  longer  needed.] 


CHAPTER    XXIX. 

NUMBEES  FROM  THIRTY  TO  FIFTY. 


§  53.    The  Number  Thirty-Two. 

Facts  to  be  taught : 

8x4  iof32  32--   8 

32 -f- 4  4x    8  iof32 

Note.   Teach  each  fact  by  itself,  and  follow  the  order  indicated 
above. 


Express  the  work  in  tbese  examples  on  the  board :  — 

If  I  have  eight  dollars  in  quarters,  how  many  quarters 
have  I  ?     (8x4  =  32.) 

Eight  gallons  are  how  many  quarts  ?     (8x4  =  32.) 

Thirty-two  quarts  will  fill  how  many  half-peck  meas- 
ures?    (32-^-4  =  8.) 

I  bought  8  pounds  of  meal  for  thirty-two  cents,  what 
was  the  meal  a  pound  ?     (^  of  32  =  4.) 

If  eight  horses  require  thirty-two  shoes,  how  many  shoes 
does  each  horse  require  ?     (\  of  32  =  4.) 

Four  pies  each  cut  into  eighths  will  make  how  many 
pieces?     (4x8  =  32.) 

If  a  man  bought  thirty- two  quarts  of  cranberries,  how 
many  pecks  did  he  buy  ?     (32  -^8  =  4.) 

Thirty-two  ox-shoes  will  shoe  how  many  oxen  all  round  ? 
(32^8  =  4.) 

How  many  feet  in  circumference  is  a  wheel  which  turns 
around  four  times  in  going  over  thirty-two  feet?  (J  of 
32  =  8.) 


368  FIRST  STEPS   IN   NUMBER. 


Ounces  in  a  Pound. 


Lift  the  larger  weight.  What  does  it  weigh?  (A 
pound.)  Find  a  stone  on  this  table  which  you  think 
weighs  a  pound.  Test  its  weight  by  these  scales.  Were 
you  right  ?  Try  again.  Each  mention  something  in  this 
room  which  weighs  a  pound. 

Mention  some  things  that  are  bought  and  sold  by  the 
pound. 

I  have  here  some  smaller  weights.  What  will  each  of 
these  weigh  ?  (An  ounce.)  Here  is  some  salt.  Put  in 
this  paper  what  you  think  will  weigh  an  ounce.  When 
the  paper  of  salt  feels  as  heavy  as  the  ounce  weight,  weigh 
it  and  see  if  it  is  more  or  less  than  an  ounce. 

Mention  some  things  that  are  sold  by  the  ounce. 

Put  the  pound  weight  in  one  scale-pan,  and  as  many 
ounces  in  the  other  as  are  required  to  balance  the  pound 
weight. 

How  many  ounces  equal  a  pound  ? 

Express  :  Sixteen  ounces  equal  one  pound. 

If  I  bought  four  ounces  of  potassium,  what  part  of  a 
pound  did  I  buy  ? 

If  I  bought  eight  ounces  of  gum  arable,  what  part  of  a 
pound  did  I  buy  ? 

If  I  bought  a  fourth  of  a  pound  of  tea,  how  many  ounces 
of  tea  did  I  buy  ? 

If  you  bought  half  of  a  pound  of  cheese,  how  many 
ounces  of  cheese  did  you  buy  ? 

I  ordered  a  pound  of  steak,  but  the  piece  brought  me 
weighed  a  pound  and  a  quarter.  How  many  ounces  did  it 
weigh  ? 

I  bought  a  pound  and  a  half  of  dates.  How  many  ounces 
did  the  dates  weigh? 

I  bought  two  pounds  of  chocolate.  How  many  ounces 
did  I  buy  ? 


NUMBERS   FROM   THIRTY    TO    FIFTY.  369 

§  54.   The  Number  Thirty-Five. 

Facts  to  be  taught : 

7x5  iof35  35-f-   7 

35-^5  5x    7  -i-of35 


Express  on  the  board : 

In  seven  weeks  bow  many  school  days  ?      (7  X  5  —  35.) 

Seven  ounces  of  potassium  at  five  cents  an  ounce  will 
cost  how  much  ?     (7x5  =  35.) 

For  thirty-five  cents  how  many  five-cent  bunches  of 
envelopes  can  I  buy  ?     (35  -^  5  =  7.) 

Thirty-five  ounces  of  liquid  will  fill  how  many  vials, 
each  containing  five  ounces  ?     (35  h-  5  =  7.) 

If  a  boy  earns  thirty-five  dollars  in  seven  months,  what 
does  he  average  to  earn  a  month  ?     (^  of  35  =  5.) 

If  I  pay  thirty-five  cents  for  seven  yards  of  cambric, 
what  is  that  a  yard  ?     (4-  of  35  =  5.) 

In  five  weeks  how  many  days  ?     (5x7  =  35.) 

In  thirty-five  days  how  many  weeks  ?     (35  ^7  =  5). 

If  I  pay  thirty -five  dollars  for  five  weeks'  board,  what 
do  I  pay  by  the  week  ?     (J  of  35  =  7.) 

Exercise  for  Review. 

Draw  two  lines  of  the  same  length  parallel  to  each  other 
and  about  an  inch  apart.  Mark  one  A  and  the  other  B. 
Divide  A  into  fourths  and  B  into  fifths.  Since  A  and  B  are 
the  same  length,  one-fifth  of  B  will  be  what  part  of  A  ? 
Compare  one-fifth  of  A  with  one-fourth  of  A,  and  tell  me 
which  is  larger. 

Which  is  larger,  one-fourth  of  an  apple  or  one- fifth  of  the 
same  apple  ?  One-fourth  of  an  orange  or  one-fifth  of  the 
same  orange  ?     One-fourth  or  one-fifth  of  a  dollar? 


370  FIRST  STEPS   IN   NUMBER. 

Find  the  sum  of: 

One  dollar  and  four  cents. 
Four  dollars  and  eleven  cents. 
Two  dollars  and  ten  cents. 
Three  dollars  and  two  cents. 
Three  dollars. 

Find  the  sum  of : 

Four  dollars  and  twenty-three  cents. 
Two  dollars  and  one  cent. 
Five  dollars  and  thirty  cents. 
Three  dollars  and  twenty-five  cents. 
Five  dollars  and  ten  cents. 

Find  the  difference  between  : 

Eight  dollars  fifty-four  cents,  and  three  dollars  thirty- 
two  cents. 

Nine  dollars  seventy-eight  cents,  and  four  dollars  three 
cents. 

Twenty-eight  dollars  forty  cents,  and  seven  dollars 
twenty  cents. 

Eighty-nine  dollars  sixty-eight  cents,  and  forty-seven 
dollars  thirty-five  cents. 

Seventy-eight  dollars  ninety-nine  cents,  and  fifty -three 
dollars  twenty-seven  cents. 

Write  the  table  of  Liquid  Measure. 
Write  the  table  of  twos. 
Who  can  write  the  table  of  threes  ? 
Two  ounces  are  what  part  of  a  pound  ? 
Two  pounds  are  how  many  ounces  ? 
Four  pecks  and  a  half  of  currants  are  how  many  quarts 
of  currants  ? 

Two  scores  of  years  are  how  many  years  ? 

Three  reams  of  paper  are  how  many  quires  of  paper  ? 


NUMBERS  FROM  THIRTY   TO   FIFTY.  371 

Four  twenty-dollar  gold  pieces  are  how  mucli  money  ? 

Four  twenty-five  cent  pieces  are  how  much  money  ? 

In  seventeen,  how  many  tens,  and  how  many  ones  besides? 
In  thirteen,  how  many  tens,  and  how  many  ones  besides? 
In  fifteen?  In  nineteen?  In  twenty-four?  In  twenty- 
seven  ?     In  forty  ?     In  fifty-three  ?     In  seventy-five  ? 

§  55.   The  Number  Thirty-Six. 
Facts  to  be  taught : 

'12  X    3  6x    6  iof36 

36--    3  36--    6  3x12 

9x    4  iof36  36-^12 

36^   4  4x    9  iof36 

iof36  36-^-9  iof36 


Express  on  the  board  : 

A  side  of  our  room  is  twelve  yards  long.  How  many 
feet  in  length  is  it  ?     (12  X  3  -  36.) 

I  bought  three  dozen  oranges  this  morning.  How  many 
oranges  did  I  buy  ?     (3x12  =  36.) 

I  have  thirty-six  cents  in  three-cent  pieces.  How  many 
three-cent  pieces  have  I  ?     (36  -r-  3  =  12.) 

I  have  here  a  stick  which  is  thirty-six  inches  long.  How 
many  feet  in  length  is  the  stick  ?     (36  -^- 12  =  3.) 

Nine  gallon-jugs  will  hold  how  many  quarts  of  vinegar? 
(9x4-36.) 

At  nine  cents  a  quarter,  what  will  a  pound  of  candy  cost? 
(4X9  =  36.) 

Thirty-six  panes  of  glass  will  supply  how  many  windows, 
if  it  takes  four  panes  for  each  window  ?     (36  -^4  =  9.) 

At  nine  cents  a  quire,  how  many  quires  of  paper  can  I 
buy  for  thirty-six  cents  ?     (36^9  =  4.) 


372  FIRST   STEPS   IN   NUMBER. 

Six  melons,  each  cut  into  sixths,  will  make  how  many- 
pieces?     (6x6  =  36.) 

Thirty-six  eggs  will  make  how  many  loaves  of  cake,  if  a 
half  dozen  is  required  for  each  loaf?     (36  -h  6  =-  6.) 

If  you  divide  a  yard  of  ribbon  into  three  equal  parts,  how 
many  inches  in  length  is  each  part?     (-^  of  36  ==  12.) 

Thirty-six  pounds  of  starch  were  put  into  four  equal 
packages.  How  many  pounds  were  in  each  package? 
(i  of  36  =  9.) 

If  six  yards  of  cloth  cost  thirty-six  cents,  what  is  the  cloth 
a  yard?     (|  of  36  =  6.) 

If  I  can  buy  nine  dozen  clothes-pins  for  thirty-six  cents, 
what  are  they  worth  a  dozen  ?     (-J-  of  36  =  4.) 

Exercise  for  Review. 

Some  silk,  some  ribbon,  and  some  ruching  together  cost 
thirty-six  cents.  The  silk  and  the  ribbon  cost  twenty-four 
cents.  The  ribbon  and  the  ruching  cost  eighteen  cents. 
What  did  each  of  the  articles  cost?  (Ruching  12  cents, 
ribbon  6  cents,  silk  18  cents.) 

We  have  a  flight  of  stairs  consisting  of  twenty  steps. 
Each  step  is  twelve  inches  broad  and  six  inches  deep.  How 
many  yards  of  carpeting  will  be  required  to  carpet  the 
stairs  ?     (10  yards.) 

How  many  plants,  a  foot  apart,  can  be  set  in  two  bor- 
ders, each  five  yards  long  ?  (32.)  In  three  borders,  each 
three  yards  long  ?     (30.) 

If  in  a  winter's  day  it  is  dark  from  half-past  four  until 
half-past  seven  the  next  morning,  how  many  hours  is  it 
from  daylight  to  dark  ?     (9  hours.) 

Eddie  had  a  ten-cent  piece,  three  five-cent  pieces,  a  three- 
cent,  and  a  two-cent  piece.  He  bought  a  kite  for  ten  cents, 
and  three  oranges  at  five  cents  apiece.  How  many  cents 
had  he  left  ?     (5  cents.) 


NUMBERS   FROM   THIRTY   TO   FIFTY.  373 

If  a  sheet  of  paper  is  doubled  four  tiraes,  how  many 
leaves  are  made  ?     (16.) 

A  long  strip  of  lead  was  cut  into  five  strips,  each  six 
inches  long,  and  there  were  three  inches  of  the  lead  left. 
How  long  was  the  strip  of  lead  ?     (33  inches.) 

A  boy  who  was  selling  lilies  sold  five  for  two  cents. 
How  much  money  did  he  receive  for  thirty  lilies?  (12 
cents.)     For  fifty  lilies  ?     (20  cents.) 

If  two  men  can  lay  a  wall  in  thirty  days,  how  long  will 
it  take  four  men  to  lay  the  wall  ?  (15  days.)  How  long 
will  it  take  six  men  ?     (10  days.) 

I  bought  some  oranges  and  some  candy  for  twenty-four 
cents.  The  oranges  cost  twice  as  much  as  the  candy.  How 
much  did  the  candy  cost  ?     (8  cents.) 

I  have  a  half  of  a  dollar  and  John  has  a  quarter  of  a 
dollar.     What  part  of  a  dollar  have  we  together  ?     (f .) 

It  will  take  a  fourth  of  a  yard  of  velvet  to  face  my  hat, 
an  eighth  of  a  yard  to  bind  it,  and  a  half  of  a  yard  for  bows. 
How  much  velvet  do  I  need  for  the  hat  ?     (|-.) 

It  takes  a  quarter  of  a  yard  of  satin  to  make  a  bag,  and 
an  eighth  of  a  yard  to  face  it.  How  much  satin  will  it  take 
all  together?  (f.)  What  will  the  satin  cost  at  eighty 
cents  a  yard  ?     (30  cents.) 

Pecks  in  a  Bushel. 

Look  at  these  two  measures.  What  do  we  call  the 
smaller  one  ?     (A  peck  measure.) 

The  larger  one  holds  a  half-bushel.  Measure  these  oats, 
and  find  how  many  pecks  make  a  half-bushel. 

Who  can  tell  how  many  pecks  make  a  whole  bushel  ? 

Write :  Four  pecks  equal  a  bushel. 

What  is  bought  by  the  bushel  ? 

A  half-bushel  of  potatoes  is  how  many  pecks  of  pota- 
toes? 


374  FIRST  STEPS   IN   NUMBER. 

A  bushel  of  peas  is  how  many  pecks  of  peas  ? 

A  bushel  of  apples  is  how  many  pecks  of  apples  ? 

A  bushel  of  nuts  is  how  many  pecks  of  nuts  ? 

Four  bushels  are  how  many  pecks? 

Six  bushels  are  how  many  pecks  ? 

Nine  bushels  are  how  many  pecks? 

Eight  bushels  are  how  many  pecks? 

Seven  bushels  are  how  many  pecks? 

Ten  bushels  are  how  many  pecks  ? 

Five  bushels  are  how  many  pecks  ? 

§  56.     The  Number  Forty, 
Facts  to  be  taught : 

■^oi^O  40-^   5         5x8  iof40 

8x    5  -J- of 40       40-^8  ■i-of40 

Express  on  the  board  : 

If  I  can  buy  ten  spools  of  thread  for  forty  cents,  what 
does  one  spool  cost  ?     (-^^  of  40  ==  4.) 

Eight  gloves  have  how  many  fingers  ?     (8  X  5  =  40.) 

How  many  dozen  peaches,  at  five  cents  a  dozen,  can  be 
bought  for  forty  cents  ?     (40  -^  5  =  8.) 

If  a  boy  earned  forty  dollars  in  eight  weeks,  how  much 
did  he  earn  in  one  week  ?     (\  of  40  =  5.) 

If  a  man  works  eight  hours  a  day,  how  many  hours  will 
he  work  in  five  days  ?     (5x8==  40.) 

If  a  bicycle  will  go  a  mile  in  eight  minutes,  how  many 
miles  will  it  go  in  forty  minutes  ?     (40  -^8  =  5.) 

Susie  recites  forty  lessons  a  week  if  she  is  at  school  five 
days  in  the  week.  How  many  lessons  does  she  recite  each 
day?     (I  of  40 -8.) 

I  bought  forty  yards  of  carpeting,  and  used  one-half  of 
it.     How  much  did  I  use?    (i of  40 -20.) 


NUMBERS   FROM   THIRTY   TO   FIFTY.  375 

§  67.    The  Number  Forty-Two. 
Facts  to  be  taught : 

7x6  I  of  42  42-v-   7 

42-V-6  6x    7  |of42 

Express  on  the  board  : 

How  many  working  days  are  there  in  seven  weeks? 
(7x6-42.) 

If  eggs  are  packed  in  layers  of  half  a  dozen  each,  how 
many  layers  will  forty-two  eggs  make  ?     (42  -r-  6  =  7.) 

If  seven  cans  will  hold  forty-two  quarts  of  milk,  what 
will  one  can  hold  ?     (-f  of  42  =  6.) 

In  six  weeks  how  many  days  ?     (6x7=  42.) 

If  we  use  a  bag  of  flour  a  week,  how  many  bags  of  flour 
do  we  use  in  forty-two  days  ?     (42  -f-  7  ==  6.) 

A  little  boy  who  works  in  a  mill  earns  forty-two  cents 
a  week.     How.  much  does  he  earn  a  day  ?     (^  of  42  =  7.) 

§  58.     The  Number  Forty-Five. 

Facts  to  be  taught : 

9x5  ^of45  45-^   9 

45-^5  5x    9  I  of  45 

Express  on  the  board : 

If  a  man  can  paint  five  pails  in  an  hour,  how  many  pails 
can  he  paint  in  nine  hours  ?     (9x5  =  45.) 

How  many  weeks  will  forty-five  pounds  of  butter  last  a 
family  when  five  pounds  are  used  a  week  ?     (45  -^5  =  9.) 

If  it  takes  forty-five  pickets  for  nine  gates,  how  many 
pickets  will  it  take  for  one  gate  ?     (^  of  45  =  5.) 

A  man  set  out  cabbage  plants,  nine  in  a  row.  How 
many  were  there  in  five  rows  ?     (5x9  =  45.) 

If  a  dozen  silver  forks  cost  nine  dollars,  how  many  dozen 
can  be  bought  for  forty-five  dollars  ?     (45  -^  9  =  5.) 


376  FIRST  STEPS  IN   NUMBER. 

If  a  newsboy  sells  forty-five  papers,  and  one-fifth  are 
weeklies  and  the  rest  dailies,  how  many  weeklies  does  he 
sell  ?     (I  of  45  =  9.)     How  many  dailies  ?     (45  -  9  =  36.) 

§  59.     First  Step  in  Multiplication  of  Fractions. 

If  it  takes  one-third  of  a  yard  of  lace  to  trim  one  sleeve, 
how  many  thirds  will  be  required  for  a  pair  of  sleeves  ?  for 
two  pairs  of  sleeves  ? 

If  a  dozen  bananas  cost  a  quarter  of  a  dollar,  how  many 
quarters  will  six  dozen  bananas  cost  ? 

If  John  earns  two-fifths  of  a  dollar  a  day,  how  many 
fifths  will  he  earn  in  a  week  ? 

It  is  three-eighths  of  a  mile  to  school.  If  I  go  over  the 
distance  four  times  a  day,  how  many  eighths  of  a  mile 
shall  I  walk  in  a  day  ? 

A  large  family  used  five-sixths  of  a  pound  of  sugar  every 
night  at  supper.  How  many  sixths  did  the  family  use  in 
a  week?     Express  this  example  on  the  board. 

Note.  If  the  pupil  has  any  difficulty  in  expressing  examples  in 
which  fractions  occur,  require  him  to  express  a  similar  example  in 
which  whole  numbers  occur,  and  he  will  perceive  the  analogy. 

Find  the  products : 


2X    1=    ^ 

2X    1=   s 

3x^  =  TTr 

3Xt^  — T-j 

4XA  =  T^ 

2xA  =  „ 

3x    1=   7 

3xA  =  TTf 

3x    1=   ^ 

3XA  =  TT 

4    X    -jV   =   TJT 

4:X-^  =  jj 

§  60.    The  Number  Forty-Eight. 

Facts  to  be  taught : 

12  X    4  48--   6              I- of  48 

48-^   4  iof48              4x12 

332-of48  6x    8  48-^12 

8x    6  48^   8             iof48 


NUMBERS   FROM   THIRTY   TO   FIFTY.  377 

Express  on  the  board  : 

Twelve  chairs  have  how  many  legs  ?     (12  X  4  =  48.) 

If  it  takes  four  rails  for  a  gate,  how  many  gates  will 
forty-eight  rails  make  ?     (48  -f-  4  =  12.) 

Forty-eight  books  were  put  into  twelve  equal  piles.  How 
many  books  were  in  each  pile  ?     (^  of  48  =  4.) 

If  one  cake  of  maple  sugar  weighs  six  pounds,  what  will 
eight  cakes  weigh  ?     (8x6==  48.) 

If  six  baskets  of  peaches  together  hold  a  peck  of  peaches, 
how  many  pecks  of  peaches  will  forty-eight  baskets  hold  ? 
(48-^6-8.) 

If  eight  bunches  of  envelopes  cost  forty-eight  cents,  what 
does  one  bunch  cost  ?     (^  of  48  =  6.) 

Six  oxen  wear  how  many  shoes  all  together  ?  (6x8  = 
48.) 

How  many  pecks  in  forty-eight  quarts  ?     (48  -1-8  =  6.) 

If  a  boy  earns  forty-eight  cents  in  six  hours,  what  is  that 
an  hour?     (|  of  48  =  8.) 

Four  dozen  oranges  are  how  many  oranges  ?  (4  X  12  = 
48.) 

In  forty-eight  inches  how  many  feet?     (48  -^- 12  =  4.) 

Forty-eight  bunches  of  matches  were  put  into  four  equal 
packages.  How  many  bunches  were  in  each  package? 
(i  of  48  =12.) 

§  61.    The  Number  Forty-Nine. 
Facts  to  be  taught : 

7x7  49-^7  |of49 

Express  on  the  board  : 

If  I  put  seven  melon  seeds  in  a  hill,  how  many  seeds  do 
I  put  in  seven  hills  ?     (7x7  =  49.) 

A  cooper  has  forty-nine  feet  of  hoop  iron.     If  it  takes 


378  FIRST  STEPS   IN  NUMBER. 

seven  feet  for  one  hoop,  how  many  hoops  can  he  make? 
(49  -f-  7  =  7.)      . 

If  seven  pounds  of  sugar  cost  forty-nine  cents,  what  does 
one  pound  cost  ?     (-f  of  49  =  7.) 

Exercise  for  Review. 

Bemark.  Application  of  numbers  in  examples  like  the  following 
is  an  important  part  of  the  work  in  Arithmetic.  It  is  not  expected 
that  the  pupil  will  solve  the  problems  by  himself.  He  will  need  to 
be  led  by  appropriate  questions  to  reason  out  the  result,  or  by  illus- 
tration to  see  the  result.  Each  example  is  a  teaching  exercise  in 
itself,  and  the  whole  exercise  is  calculated  to  teach  the  pupil  how  to 
apply  his  knowledge  of  numbers.  The  exercise  is  a  test  exercise  only 
in  the  sense  that  it  tests  knowledge  of  facts.  The  examples  are  not 
too  difficult  for  this  grade  of  work. 

A  man  who  earned  thirty  dollars  a  week  paid  ten  dollars 
a  week  for  board.  Another  man  earned  but  twenty-five 
dollars  a  week,  and  paid  four  dollars  a  week  for  board. 
Which  one  was  better  off  at  the  end  of  the  week  ? 

A  man  counting  his  eggs  for  market  found  he  had  half  a 
hundred.  He  kept  two  for  his  own  use,  and  packed  the 
rest  in  layers  of  half  a  dozen  each.  How  many  layers  had 
he? 

John  earns  three  dollars  a  week.  If  he  spends  one 
dollar  one  week,  three  dollars  the  next  week,  and  five  the 
next  week,  how  much  money  has  he  left  from  his  three 
weeks'  earnings  ?     What  are  his  average  expenses  a  week  ? 

If  I  spend  ten  dollars  one  week,  twelve  dollars  the  next 
week,  and  eleven  dollars  the  next  week,  what  are  my  aver- 
age expenses  per  week  ? 

Nellie  had  thirty  pretty  buttons  and  Elsie  had  ten  but- 
tons. Nellie  agreed  to  give  Elsie  enough  buttons  so  that 
each  should  have  the  same  number  if  Elsie  would  exchange 
some  of  her  buttons  for  Nellie's.  How  many  buttons  did 
Nellie  have  after  she  had  done  as  she  agreed  ? 


NUMBERS   FROM  THIRTY  TO    FIFTY.  379 

A  garden  plat  nine  feet  by  six  feet  was  bordered  by  a 
walk  two  feet  wide.  How  much  farther  was  it  around  the 
outside  of  the  walk  than  around  the  garden  plat  ? 

While  out  shopping  this  morning  I  spent  half  the  money 
in  my  purse.  I  had  five  dollars  when  I  returned  home. 
How  much  money  did  I  spend  ? 

After  spending  a  fourth  of  her  money  Annie  had  twelve 
cents  left.     How  many  cents  had  she  at  first  ? 

After  Harry  had  done  a  third  of  his  examples  he  had 
eighteen  more  to  do.    How  many  had  he  to  do  all  together  ? 

A  little  girl's  car-fare  was  fifteen  cents,  and  her  mamma's 
was  twice  as  much.     How  much  was  the  fare  for  both  ? 

John  guessed  that  a  pumpkin  weighed  ten  pounds  and 
four  ounces.  George  guessed  it  weighed  ten  pounds  and 
ten  ounces.  Neither  was  right,  but  one  was  just  as  nearly 
right  as  the  other.     How  much  did  the  pumpkin  weigh  ? 

After  spending  a  quarter  of  a  dollar  I  had  three  times 
as  much  money  in  my  purse  as  I  spent.  How  much  money 
had  I  at  first  ? 

A  wood-sawyer  had  sticks  of  wood  four  feet  long  which 
he  was  to  cut  into  sticks  a  foot  long.  How  many  cuts  did 
he  make  in  sawing  a  dozen  sticks  of  wood  ?  How  many 
sticks  did  he  make  ? 

I  bought  eight  yards  of  cloth  at  six  cents  a  yard,  and 
gave  in  payment  a  quarter  of  a  dollar  and  three  ten-cent 
pieces.     How  much  change  ought  I  to  receive  ? 

Susie  is  fifteen  years  old  and  her  brother  is  ten  years 
old.     How  old  was  Susie  when  twice  as  old  as  her  brother  ? 

Johnnie  is  five  years  old  and  his  father  is  thirty  years 
old.  How  old  will  Johnnie  be  when  half  as  old  as  his 
father? 

James  and  his  sister  went  berrying  one  day.  At  night, 
after  their  berries  were  picked  over,  they  turned  them  into 
some  measures  to  see  how  many  they  had.     The  berries 


380  FIRST  STEPS   IN   NUMBER. 

filled  a  half-busliel  measure,  a  peck  measure,  a  two-quart 
measure,  a  quart  measure,  and  a  pint  measure.  How  many- 
quarts  of  berries  had  they  ? 

If  there  was  an  animal  whose  number  of  eyes  doubled 
each  year  he  lived,  and  who  had  two  eyes  to  begin  with, 
how  many  eyes  had  he  in  five  years  ? 

I  got  a  hundred  dollars  from  the  bank  in  six  bills.  Two 
of  the  bills  were  ten  dollars  each.  What  was  each  of  the 
other  bills  if  they  were  each  for  the  same  amount  ? 

A  man  spent  six-eighths  of  what  he  earned.  What  part 
of  his  earnings  had  he  left  ?  If  he  had  spent  seven-ninths 
of  his  earnings,  what  part  would  he  have  had  left  ?  If  he 
had  spent  six-sevenths,  what  part  would  he  have  had  left  ? 

Two  boats  are  fifty  miles  apart,  and  are  sailing  toward 
each  other.  One  sails  at  the  rate  of  six  miles  an  hour,  and 
the  other  at  the  rate  of  four  miles  an  hour.  In  how  many 
hours  will  they  pass  each  other  ? 

Two  boats  are  sailing  in  the  same  direction  and  are  ten 
miles  apart,  but  the  one  that  is  behind  goes  two  miles  an 
hour  faster  than  the  one  ahead.  How  many  hours  will  it 
take  the  boat  that  is  behind  to  make  up  the  ten  miles,  and 
so  catch  up  with  the  other  boat  ? 

One  man  earns  two  hundred  dollars  a  month,  but  has 
work  only  half  of  the  year.  Another  man  earns  a  hundred 
dollars  a  month,  and  works  every  month  in  the  year.  How 
do  the  earnings  of  the  two  men  for  a  year  compare  ? 

How  many  strokes  does  a  clock  give  in  twelve  hours  ? 

We  have  a  clock  which  strikes  every  hour,  and  strikes 
one  at  quarter  past,  two  at  half-past,  and  three  at  quarter 
of  the  hour.  How  many  strokes  does  such  a  clock  give 
from  ^Ye  minutes  past  twelve  to  five  minutes  past  six  ? 

How  many  yards  of  carpeting  a  yard  wide  will  be  needed 
to  carpet  a  room  five  yards  long  and  five  yards  wide  ? 

How  many  yards  of  carpeting  a  yard  wide  will  it  take 


NUMBERS   FROM   THIRTY   TO   FIFTY.  3gl 

to  carpet  a  hallway  that  is  a  yard  and  a  half  wide  and  six 
yards  long? 

How  many  yards  of  cloth  half  a  yard  wide  will  it  take 
to  line  a  box  that  is  a  yard  long,  a  half  a  yard  wide,  and  a 
half  a  yard  deep  ? 

If  a  wax-plant  doubled  its  number  of  blossoms  each 
year,  and  had  two  blossoms  the  first  year,  how  many  blos- 
soms had  it  the  seventh  year  ? 

If  you  divide  a  line  into  two  parts,  so  that  one  part  shall 
be  twice  as  large  as  the  other,  what  fraction  of  the  whole 
line  is  each  part  ? 

After  dividing  thirteen  by  four,  what  part  of  four  shall  I 
have  left? 

After  dividing  fifteen  by  four,  what  part  of  four  shall  I 
have  left? 

After  dividing  seventeen  by  three,  what  part  of  three 
shall  I  have  left  ? 

After  dividing  nineteen  by  six,  what  part  of  six  shall  I 
have  left?  after  dividing  twenty  by  six?  twenty-two  by 
six  ?  twenty-five  by  six  ? 

If  I  divide  two  apples  equally  among  four  boys,  what 
part  of  an  apple  shall  I  give  to  each  ? 

If  you  and  Susie  and  I  had  each  three-quarters  of  a  dol- 
lar, Low  many  dollars  should  we  have  together  ? 

If  a  boy  earned  three-quarters  of  a  dollar  a  day,  how 
much  would  he  earn  in  a  week  ? 

If  it  takes  two-fifths  of  a  yard  of  ribbon  for  a  bow,  how 
much  ribbon  will  be  needed  for  five  bows  ?  for  ten  bows  ? 

If  you  put  a  bushel  of  apples  into  four  baskets,  each 
holding  the  same  quantity,  how  many  quarts  does  each 
basket  hold  ? 

My  album  will  hold  four  pictures  on  a  page.  How 
many  pictures  will  the  album  hold  if  there  are  six  leaves  in 
it? 


382  FIKST   STEPS   IN   NUMBER. 

If  it  takes  forty  yards  of  carpeting  a  yard  wide  for  a 
room  five  yards  wide,  how  long  is  the  room  ? 

If  sugar  that  cost  seven  cents  a  pound  is  sold  at  ten  cents 
a  pound,  how  much  is  gained  on  thirteen  pounds  ? 

If  the  material  for  a  dress  costs  ten  dollars,  and  the 
trimmings  and  making  cost  twice  as  much,  how  much  does 
the  dress  cost  ? 

A  man  bought  an  old  table  for  five  dollars.  He  paid 
two  dollars  for  having  it  scraped,  and  sold  it  for  ten  dol- 
lars.    How  much  did  he  gain  ? 

A  farmer's  wife  sold  four  dozen  eggs  at  a  quarter  of  a 
dollar  a  dozen,  and  took  her  pay  in  cotton  cloth  at  ten 
cents  a  yard.     How  many  yards  did  she  get  ? 

My  watch  will  run  from  eight  o'clock  in  the  morning 
until  twelve  o'clock  at  night  the  next  day.  How  many 
hours  will  my  watch  run  ? 

If  I  leave  the  school-house  at  five  o'clock  at  night,  and 
am  there  at  half-past  eight  in  the  morning,  how  many  hours 
from  the  time  I  leave  the  school-house  until  I  return  ? 

If  a  locomotive  goes  at  the  rate  of  two  miles  in  three 
minutes,  how  far  will  it  go  in  fifteen  minutes  ?  in  twenty- 
one  minutes  ?  in  eighteen  minutes  ?  in  thirty  minutes  ?  At 
the  same  rate,  how  long  will  it  take  the  locomotive  to  go 
four  miles  ?  eight  miles  ?  sixteen  miles  ? 

If  you  make  a  little  book  by  doubling  a  piece  of  paper 
six  times,  how  many  leaves  Avill  your  book  have  ?  How 
many  pages  ? 

If  there  are  fifty  pages  in  a  book,  what  are  the  two 
middle  pages  numbered  ?  If  there  are  fifty  leaves  in  a 
book,  what  are  the  two  middle  pages  numbered  ? 

A  boy  earned  four  dollars  a  week.  How  much  money 
had  he  at  the  end  of  twelve  weeks  if  he  had  spent  two 
weeks*  earnings? 

Four  cubes  have  how  many  faces  ?  have  how  many  cor- 
ners ?  have  how  many  edges  ? 


NUMBERS  FROM   THIRTY  TO   FIFTY.  383 

At  the  rate  of  a  half-cent  for  every  ounce,  how  much 
will  it  cost  to  send  a  package  weighing  two  pounds  ? 

Nellie  is  three  years  old  the  eleventh  of  September; 
Johnnie  is  six  years  old  the  seventh  of  the  same  month. 
How  much  older  than  Nellie  is  Johnnie  ? 

Ida  is  nine  years  old  the  ninth  of  May ;  Jennie  is  seven- 
teen years  old  the  ninth  of  September.  How  much  older 
than  Ida  is  Jennie  ? 

A  man  saved  thirty-two  dollars  one  month,  half  as  much 
the  next  month,  and  spent  eight  dollars  more  than  he 
earned  the  next  month.  How  much  money  had  he  at  the 
end  of  the  three  months? 

A  boy  who  earned  three  dollars  a  week  spent  two  dol- 
lars one  week,  one  dollar  another  week,  and  a  half  of  a 
dollar  each  of  two  other  weeks.  How  much  had  he  saved 
at  the  end  of  four  weeks  ? 

If  I  draw  as  large  a  square  as  I  can  in  a  circle  that  is 
twelve  inches  across,  how  many  inches  will  it  be  across  the 
square  from  corner  to  corner  ? 

How  many  square  tiles,  six  inches  on  a  side,  can  I  place 
around  the  outside  of  a  hearth  that  is  four  feet  long  and 
two  feet  deep  ?  Kepresent  the  hearth  on  the  board,  and 
see  if  you  are  right.  If  the  tiles  were  only  four  inches  on 
a  side,  how  many  could  I  place  around  the  outside? 

Henry's  hoop  is  six  feet  round  the  outside.  If  it  turns 
round  eight  times  without  tumbling  over,  how  much  ground 
does  it  pass  over? 

How  many  desks,  each  occupying  two  feet  of  room,  and 
placed  two  feet  apart,  can  be  set  across  a  room  that  is 
thirty-six  feet  wide,  if  the  two  end  desks  are  each  three 
feet  from  the  wall  ? 


CHAPTER  XXX. 

PROCESSES  IN  WRITTEN  ARITHMETIC  CONTINUED. 


§  62.    Second  Step  in  Addition. 

When  the  sum  of  the  ones  exceeds  nine. 

Three  boys  were  counting  their  money.  One  boy  had  a 
quarter  of  a  dollar,  another  boy  had  ten  cents  more,  and 
the  third  boy  had  thirty-eight  cents.  Let  us  see  how 
much  money  they  had  all  together.  Show  me  each  of  the 
numbers.  What  will  you  do  first,  Willie  ?  (Find  the  sum 
of  the  ones.)  How  many  ones?  (Eighteen.)  In  eighteen 
how  many  tens  ?  Put  this  rubber  band  about  the  ten. 
Who  thinks  what  to  do  with  this  ten?  (Put  it  with  our 
other  tens.)  How  many  tens  will  you  then  have  ?  How 
much  money  had  the  three  boys  together  ? 

A  farmer  sent  to  market  a  dozen  and  a  half  bushels  of 
potatoes  at  one  time,  two  dozen  bushels  at  another  time, 
and  three  dozen  bushels  at  another  time.  Let  us  find  how 
many  bushels  he  sent  all  together.  Of  what  will  you  find 
the  sum  first,  Eddie?  (Of  the  ones.)  How  many^ones? 
How  many  tens  in  twenty-two  ?  Put  a  rubber  band  about 
each  ten.  What  will  you  do  with  these  two  tens,  Annie? 
How  many  tens  will  you  then  have  ?  How  many  bushels 
of  potatoes  did  the  farmer  send  to  market  ? 

Note.  As  soon  as  the  children  can  readily  find  the  answers  to 
such  examples  as  the  above  by  means  of  the  objects,  send  them  to  the 
board  to  perform  similar  examples.     Give  much  practice. 


PROCESSES   IN   WRITTEN 

ARITHMETIC  ' 

Other  steps  in  addition : 

736 

1436 

254 

3798 

76 

2764 

39 

1978 

385 


§  63.    Second  Step  in  Subtraction. 

When  the  number  in  the  right-hand  order  of  the  minue^id 
is  less  than  the  number  in  the  corresponding  order  of  the 
subtrahend. 

There  were  fifty-two  children  in  a  room,  but  a  class  of 
twenty-eight .  was  excused.  We  want  to  find  how  many 
were  left  in  the  room.  Show  me  the  number  in  the  room 
before  any  left  the  room.  Subtract  the  number  of  ones 
first.  How  many  ones  must  you  subtract?  (8.)  Who 
knows  where  to  look  for  more  ones  ?  (Break  a  bundle  of 
tens.)  Yes,  break  a  bundle  of  tens  and  put  the  ten  with 
the  ones.  Now  subtract  eight.  How  many  ones  have  you 
left?  (4.)  How  many  tens  must  you  subtract?  (2.) 
Subtracting  the  two  tens,  what  number  have  you  left? 
(24.)     How  many  children  then  remained  in  the  room  ? 

Note.  Give  similar  examples  for  work  with  objects  until  the 
pupils  can  readily  find  the  answer.  Take  care  to  have  the  work  per- 
formed in  the  right  order,  viz. :  First.  Take  a  ten  and  unite  it  with 
the  ones  of  the  minuend.  Second.  Subtract  the  given  number  of 
ones.     Third.     Subtract  the  tens. 

Preparatory  to  passing  from  work  with  the  objects  to  work  with 
figures,  question  the  pupil  in  regard  to  the  order  he  follows,  thus : 
In  finding  the  difference  between  seventy-six  and  thirty -seven,  what 
do  you  do  first  ?  (Take  a  ten  and  put  it  with  the  ones.)  What 
next?     (Subtract  seven.)    What  next?    (Subtract  three  tens.) 

Take  this  example  at  the  board  : 

A  man  who  had  eighty-three  chickens  sold  fifty-nine. 
How  many  had  he  left  ? 


386  FIEST  STEPS   IN   NUMBER. 

(When  the  work  is  completed  it  will  stand  on  the 
irt  board  in  the  form  shown  in  the  margin.  After  some 
59  practice  the  pupil  will  not  need  to  express  the 
Y^     ''  borrowing,"  but  may  carry  on  the  work  mentally.) 

Other  steps  in  subtraction  : 

350  702  6000 

-  105  -  57  -  999 


§  64.    Second  Step  in  Multiplication. 

When  the  multiplier  consists  of  one  figure,  and  the  prod- 
uct  of  the  numher  in  the  lowest  order  of  the  multiplicand  hy 
the  mAiltipliefi-  exceeds  nine, 

I  had  a  square  box  that  was  sixteen  inches  on  a  side.  I 
want  you  to  tell  me  how  far  it  was  round  the  box.  What 
will  you  find  first  ?  (Four  sixes.)  How  many  tens  in  your 
answer?  Put  a  rubber  band  about  each  ten.  What  will 
you  find  next  ?  (Four  tens.)  What  will  you  do  with  the 
two  tens  you  found  in  twenty-four  ?  (Add  them  to  the 
four  tens.)     How  many  inches  round  the  box?     (64.) 

(Begin  with  work  on  the  board  as  soon  as  the  pupil  com- 
prehends that  he  is  to  separate  the  tens  from  the  ones 
*^^  in  the  product  of  units  by  units,  and  that  he  is  to  add 
-jT-  these  tens  to  the  product  of  the  tens.  It  is  well  to 
-j  gQ  have  the  partial  products  expressed  separately  at  first, 
Tqq  as  shown  in  the  work  written  in  the  margin.  In  a 
short  time  the  pupil  will  learn  to  **  carry  "  mentally, 
and  express  only  the  entire  product.) 

Find  the  products  : 

46,  59  27  84 

7  6  8  9 


CHAPTER  XXXI. 

NUMBERS  FROM  FIFTY  TO  SIXTY. 


§  65.    The  Number  Fifty-Four. 

Facts  to  be  taught : 

9X6 

|of54 

54- 

^   9 

54--6 

6x    9 

i' 

3f54 

§  66.     The  Number  Fifty-Six. 

Facts  to  be  taught : 

8x7  iof56  56h-   8 

56 --7  7x    8  4- of 56 

§  67.    The  Number  Sixty. 
Facts  to  be  taught : 

12x    5  5x12  Jof60 

60^    5  60^12  iof60 

^of60  -J-of60  Jyof60 

Exercise  for  Review. 

How  many  months  in  four  years  ? 

Counting  four  weeks  and  two  days  to  a  month,  how 
many  weeks  are  in  a  year  ? 

A  quire  of  paper  is  usually  divided  into  four  equal  pack- 
ages. How  many  sheets  of  paper  are  in  each  package? 
How  many  sheets  of  paper  in  eight  such  packages?  How 
inany  quires? 


388  FIRST  STEPS  IN   NUMBER. 

A  man  bought  six  pecks  of  cranberries.  If  bis  family 
ate  a  quart  a  day,  bow  many  days  did  tbey  last  ? 

A  cbeese  wbicb  weigbed  forty-eigbt  pounds  was  cut  into 
quarters.  What  did  each  quarter  weigh  ?  What  did  half 
of  the  cbeese  weigh  ? 

What  fiye  equal  pieces  of  money  make  fifty  cents  ?  What 
ten  equal  pieces  ?  What  two  equal  pieces  ?  What  twenty- 
five  equal  pieces  ?     What  fifty  equal  pieces  ? 

Nine  flies  have  bow  many  legs  all  together? 

If  it  takes  a  half-dozen  eggs  to  make  a  loaf  of  cake,  how 
many  eggs  will  it  take  to  make  nine  loaves  ? 

If  a  man  works  at  his  trade  nine  hours  a  day,  how  many 
hours  does  be  work  in  a  week  ? 

If  I  can  buy  a  ticket  and  a  half  for  six  cents,  how  many 
tickets  can  I  buy  for  fifty-four  cents  ? 

A  roll  of  wall-paper  fifty-four  feet  long  will  make  how 
many  strips,  if  our  room  is  nine  feet  high  ? 

A  chamber-set  was  valued  at  fifty-four  dollars,  but,  being 
damaged,  the  price  was  reduced  one-sixth.  What  then 
was  its  price  ? 

There  were  fifty-four  pounds  of  butter  in  a  tub.  How 
much  remained  when  one-ninth  of  it  had  been  used  ? 

How  many  school-days  in  eleven  weeks  ? 

If  a  star-fish  has  five  arms,  how  many  arms  have  eleven 
star-fish  ? 

I  bought  five  sticks  of  braid,  each  of  which  lacked  one 
yard  of  containing  a  dozen  yards.  How  many  yards  of 
braid  were  in  the  five  sticks  together  ? 

Of  fifty-five  plants  which  the  gardener  set  out  this  spring, 
one-fifth  was  killed  by  the  frost.    How  many  were  killed  ? 

How  many  days  in  seven  weeks  ?  in  eight  weeks  ? 

I  bought  eight  yards  of  cambric  at  seven  cents  a  yard, 
and  gave  in  payment  a  fifty-cent  coin  and  a  ten-cent  coin. 
What  change  ought  I  to  receive  ? 


NUMBERS   FROM  FIFTY   TO  SIXTY.  389 

How  long  will  seven  pecks  of  oats  last  a  horse  if  he  eats 
seven  quarts  a  day? 

A  man  paid  fifty-six  cents  for  peaches,  at  eight  cents  a 
dozen.  Two  dozen  decayed,  and  he  sold  the  rest  at  twelve 
cents  a  dozen.     Did  he  gain  or  lose,  and  how  much  ? 

A  man  bought  a  chamber-set  for  fifty-six  dollars,  and  a 
rocking-chair  for  one-eighth  as  much.  What  did  he  pay 
for  both  together. 

A  man  bought  a  cooking-range  for  fifty-six  dollars,  and 
a  small  oil-stove  for  one-seventh  as  much.  What  was  the 
difiference  in  price  ? 

A  man  who  sells  shoe-strings  at  six  cents  a  dozen  gains 
a  cent  on  each  dozen  ?     What  did  twelve  dozen  cost  him  ? 

In  five  feet  how  many  inches  ? 

In  five  years  how  many  months  ? 

In  five  dozen  how  many  things  ? 

If  you  can  buy  two  apples  for  fiye  cents,  how  many  apples 
can  you  buy  for  sixty  cents  ? 

A  newsboy  buys  eight  papers  for  twelve  cents.  How 
many  papers  will  he  get  for  sixty  cents  ?  If  he  sells  his 
papers  for  two  cents  apiece,  what  does  he  gain  on  eight 
papers  ?  on  sixteen  papers  ?  on  twenty-four  papers  ?  How 
many  dozen  papers  must  he  sell  to  gain  sixty  cents  ? 

In  sixty  school-days  how  many  school- weeks  ? 

If  it  takes  sixty  tiles  for  a  fire-place,  how  many  dozen 
tiles  does  it  take  ? 

If  your  vacation  is  sixty  days  long,  and  you  spend  a  fifth 
of  the  time  at  home,  how  many  weeks  are  you  at  home  ? 

What  twelve  equal  numbers  make  sixty  ?  What  then  is 
one-twelfth  of  sixty  ? 

What  piece  of  money  is  one-twelfth  of  sixty  cents  ? 

If  in  a  term  of  twelve  weeks  a  boy  is  absent  one-sixth  of 
the  number  of  school-days,  how  many  school-weeks  is  he 
absent  ? 


390  FIRST  STEPS   IK   NUMBER. 

When  tea  is  sixty  cents  a  pound,  wliat  will  one-sixth  of 
a  pound  cost  ?  one-tenth  of  a  pound  ?  one-half  of  a  pound  ? 

My  expenses  for  one  month  were  sixty  dollars.  I  spent 
one-half  of  the  money  for  board,  one-fifth  for  clothing,  one- 
sixth  for  books  and  stationery,  one-tenth  for  hired  labor, 
and  the  rest  in  travelling.  What  did  I  spend  for  each 
item? 

If  a  man  buys  old  rubber  at  a  half  a  cent  a  pound,  what 
will  he  pay  for  sixty  pounds?  for  fifty  pounds?  How 
much  rubber  will  thirty  cents  buy  ?  twenty-five  cents  ? 

How  much  will  a  man  gain  on  four  pounds  of  rubber  if 
he  buys  it  at  a  half  a  cent  a  pound,  and  makes  it  into  toys 
which  he  sells  at  twenty  cents  a  pound,  if  there  is  a  waste 
of  one  pound  ? 

If  a  loaf  of  bread  costs  the  baker  seven  cents,  and  he 
sells  it  for  ten  cents,  how  much  does  he  gain  on  a  dozen 
loaves  of  bread  ? 

A  Second  of  Time. 

What  have  I  here?  (A  weight  attached  to  a  string.) 
The  string  is  thirty-nine  inches  long.  I  will  hang  it  on 
this  hook,  and  make  the  weight  swing.  Whenever  it  passes 
just  under  the  hook  you  may  count. 

How  many  have  you  counted  ?     (10.) 

Between  each  of  your  counts  was  a  second  of  time.  How 
many  seconds  was  the  weight  swinging  ? 

As  I  swing  the  weight  again  you  may  say  aloud,  but 
softly,  one  second,  two  seconds,  three  seconds,  and  so  on. 
How  many  seconds  did  the  weight  swing  this  time  ?     (15.) 

You  may  now  count  silently,  and  when  twenty  seconds 
have  passed,  Eddie  may  stop  the  weight.  Was  he  right, 
class  ? 

When  thirty  seconds  have  passed,  Annie  may  stop  the 
weight. 


NUMBERS   FROM   FIFTY   TO   SIXTY.  391 

When  forty-five  seconds  liave  passed,  Walter  may  stop 
the  weight. 

Count  sixty  seconds  now,  and  then  I  will  stop  the  weight. 

You  may  see  how  many  seconds  it  takes  me  to  walk  to 
the  back  of  the  room  ;  how  many  seconds  it  takes  Minnie 
to  make  her  slate  clean  ;  how  many  seconds  it  takes  Walter 
to  write  his  name. 

Annie  may  turn  so  that  she  cannot  see  the  weight ;  count 
ten  seconds  and  turn  back  again.  The  others  may  count 
ten  seconds  by  the  swinging  of  the  weight.  Did  Annie 
count  right  ?     (She  counted  too  fast.) 

Emily  may  turn  and  count  fifteen  seconds.  Was  she 
right?     (She  counted  too  fast.) 

Walter  may  turn  and  count  thirty  seconds.  Was  Walter 
right  ?     (He  was  one  second  ahead.) 

Half  of  the  class  may  turn  and  count  sixty  seconds.  The 
other  half  count  by  the  swinging  of  the  weight,  and  see  who 
of  those  who  turn  are  right. 

All  shut  your  eyes,  and  when  you  think  sixty  seconds 
have  passed,  you  may  raise  hands.  I  will  tell  you  who  is 
nearest  right. 

Seconds  in  a  Minute. 

Look  at  the  smallest  hand  of  my  watch.  You  may  tell 
me  when  it  has  gone  entirely  round  the  little  circle,  and  I 
will  tell  you  how  many  swings  the  weight  has  made. 

I  will  now  watch  the  little  hand,  and  you  may  count  the 
swings.     Do  you  find  it  to  be  sixty  times,  too? 

How  many  seconds  then  does  it  take  the  little  hand  to 
go  entirely  round  the  circle? 

Who  knows  what  name  we  give  to  sixty  seconds  of  time  ? 
Carrie  says  it  is  a  minute  of  time,  and  that  is  right. 

Write  on  the  board  :  Sixty  seconds  make  a  minute. 

Who  thinks  he  can  tell  when  a  minute  of  time  is  gone, 


392      '  FIRST  STEPS   IN  NUMBER. 

without  looking  at  the  watch  or  counting  by  the  weight  ? 
We  will  let  John  try.  He  may  step  outside  the  door  and 
wait  just  a  minute.  The  others  may  see  by  the  watch  or 
by  the  weight  how  long  he  is  gone.  How  long  was  he 
gone  ?     (A  half  of  a  minute.) 

Step  to  the  board  and  write  your  names  as  many  times 
as  you  can  in  a  minute.  When  you  have  been  writing  a 
minute  I  will  say,  Now. 

See  how  many  different  words  you  can  write  in  a  minute. 

See  how  many  words  that  rhyme  you  can  write  in  a 
minute  ? 

See  how  long  a  column  of  numbers  you  can  write  and 
add  in  a  minute. 

See  if  you  can  draw  a  square,  an  equilateral  triangle,  and 
a  rectangle  in  a  minute. 

Make  all  the  marks  of  punctuation,  and  all  the  letters  of 
the  alphabet  in  a  minute  if  you  can. 

Count  silently  as  high  as  you  can  in  a  minute. 

How  many  seconds  in  half  a  minute  ?  in  one-fifth  of  a 
minute  ?  in  one-sixth  of  a  minute  ?  in  one-tenth  of  a  min- 
ute ?  in  one-twelfth  of  a  minute  ? 

Ten  seconds  are  what  part  of  a  minute  ? 

Six  seconds  are  what  part  of  a  minute  ? 

Twelve  seconds  are  what  part  of  a  minute  ? 

Five  seconds  are  what  part  of  a  minute  ? 

Fifteen  seconds  are  what  part  of  a  minute  ? 

Twenty  seconds  are  what  part  of  a  minute  ? 

Minutes  in  an  Hour. 

Who  knows  how  long  it  takes  the  long  hand  to  go  round 
the  face  of  the  clock  ?  You  are  all  right.  It  does  take  an 
hour. 

Who  knows  how  many  minutes  it  takes  the  long  hand  to 
go  from  twelve  to  one  ?     It  does  take  five  minutes.     How 


NUMBEKS   FROM   FIFTY   TO  SIXTY.  393 

many  minutes  does  it  take  the  long  hand  to  go  from  one  to 
two  ?  from  two  to  three  ?  from  three  to  four  ?  How  many- 
minutes  does  it  take  the  long  hand  to  go  from  any  figure  to 
the  next  figure  ?  Let  us  see  now  if  we  can  count  up  the 
number  of  minutes  it  takes  the  long  hand  to  go  round  the 
face  of  the  clock.  If  it  takes  five  minutes  to  move  from 
figure  to  figure,  how  many  fives  must  we  count  ?  Twelve 
fives  make  how  many  ?  Then  how  many  minutes  does  it 
take  the  long  hand  to  go  round  the  face  of  the  clock  ?  How 
many  minutes  then  in  an  hour? 

"Write  on  the  board  :  Sixty  minutes  make  an  hour. 

How  many  minutes  in  half  an  hour  ?  in  one-quarter  of 
an  hour  ?  in  one-sixth  of  an  hour  ?  in  one-twelfth  of  an 
hour  ?  in  one-third  of  an  hour  ? 

How  many  minutes  in  two  hours?  in  three  hours?  in 
four  hours  ? 

How  many  minutes  are  you  in  school  if  the  session  is 
five  hours? 

If  I  stay  an  hour  longer,  how  many  minutes  am  I  in 
school  ? 

When  the  long  hand  is  at  one,  how  many  minutes  past 
the  hour  is  it  ?  When  the  long  hand  is  at  two,  how  many 
minutes  past  the  hour  is  it  ?  When  it  is  at  three  ?  at  four  ? 
at  five  ?  at  six  ? 

How  many  minutes  of  the  hour  is  it  when  the  long  hand 
is  at  seven  ?  at  eight  ?  at  nine  ?  at  ten  ?  at  eleven  ? 

At  what  figure  does  the  long  hand  point  at  quarter  past 
the  hour  ?  at  half  past  the  hour  ?  at  quarter  of  the  hour  ?  at 
twenty  minutes  past  the  hour  ?  at  twenty  minutes  of  the 
hour? 

Complete  this  table : 

60  seconds  =  7  days       = 

60  minutes  =  4  weeks  and  2  days  = 

24  hours      =  12  months  = 


CHAPTER   XXXIL 

NUMBERS  FROM  SIXTY  TO  SEVENTY. 


§  68.    The  Number  Sixty-Three. 

Facts  to  be  taught : 

9x7  iof63  63-^-9 

63-^7  7x    9  I  of  63 

§  69.     The  Number  Sixty-Four. 

Facts  to  be  taught : 

8x8  1-  of  64 

64-^8  I  of  64 

Exercise  for  Review. 

In  nine  weeks  how  many  days  ? 

In  nine  weeks  how  many  working-days  ? 

In  nine  weeks  how  many  school-days  ? 

A  man  pays  three  dollars  a  week  for  his  room,  and  four 
dollars  a  week  for  board.   "What  does  he  pay  in  nine  weeks  ? 

If  I  pay  a  dollar  a  day  for  board,  what  do  I  pay  for  nine 
weeks'  board? 

A  farmer  sold  a  dozen  eggs  for  twenty-three  cents,  and 
^Ye  quarts  of  berries  at  eight  cents  a  quart,  and  took  in 
payment  sugar  at  seven  cents  a  pound.  How  many  pounds 
did  he  receive  ? 

If  it  took  a  man  sixty-three  days  to  do  a  piece  of  work, 
how  long  did  it  take  him  to  do  one-ninth  of  the  work  ? 


NUMBERS   FROM  SIXTY   TO  SEVENTY.  395 

If  I  pay  sixty-three  dollars  for  nine  weeks'  board,  what 
is  that  a  day  ? 

When  bananas  are  five  cents  each,  and  oranges  four 
cents,  what  must  I  pay  for  seven  of  each  ? 

One  room  is  four  yards  long,  and  another  room  five 
yards  long.  How  many  yards  of  carpeting  will  it  take  for 
both  rooms  if  each  takes  seven  strips  ? 

Twenty-one  yards  of  wall-paper  will  cut  how  many 
strips  of  paper  each  nine  feet  long  ? 

A  man  who  is  three  score  and  three  years  old  is  seven 
times  as  old  as  his  grandson.     How  old  is  his  grandson  ? 

If  a  man  earns  sixty-three  dollars  a  month,  and  spends 
fifty-six  dollars,  how  many  months  will  it  take  him  to  save 
a  month's  wages  ?    What  part  of  a  year  ? 

A  stationer  who  buys  blank-books  for  forty-one  cents 
sells  them  at  fifty  cents  each.  If  in  one  day  he  gains  sixty- 
three  cents  from  the  sale  of  these  books,  how  many  books 
does  he  sell  that  day  ? 

A  boy  who  earns  eight  cents  an  hour  works  eight  hours 
a  day.  How  much  does  he  earn  in  a  day  ?  If  he  spends 
fourteen  cents  a  day,  how  much  money  will  he  have  at 
the  end  of  the  week  ? 

What  must  I  pay  for  a  peck  of  cherries  at  eight  cents  a 
quart?  If  they  shrink  one-half  in  cooking,  how  many  pint 
jars  of  sauce  shall  I  have  ?  If  cherries  cost  eleven  cents  a 
pint  when  canned,  how  much  money  do  I  save  in  putting 
up  a  peck  of  cherries  for  myself? 

If  a  glazier  has  sixty-four  panes  of  glass,  how  many  win- 
dows each  containing  eight  panes  can  he  fill  ? 

If  it  takes  a  steamer  eight  days  to  make  a  trip,  how 
many  trips  will  it  make  in  two  months  of  thirty-one  days 
each,  and  two  more  days  ? 

If  sixty-four  pounds  of  flour  will  last  a  family  eighi, 
weeks,  how  much  does  the  family  use  in  one  week  ? 


396  FIRST  STEPS  IN  NUMBER. 

A  bicycle  goes  sixty-four  miles  in  eight  hours.  What  ie 
the  rate  per  hour  ? 

There  are  thirty-two  quarts  in  a  bushel.  How  many 
quarts  in  two  bushels  ? 

A  two-pound  weight  equals  thirty-two  ounces.  How 
many  ounces  will  a  four-pound  weight  equal  ? 

If  a  bushel  of  beans  weighs  sixty-four  pounds,  what  will 
a  half-bushel  weigh?  What  will  a  peck  weigh?  What 
will  a  quart  weigh  ? 

If  a  pound  of  cake  costs  the  baker  thirty-five  cents,  and 
he  sells  it  for  forty  cents,  what  does  he  gain  on  a  dozen 
pounds  of  cake  ? 

If  a  sick  man  must  take  two  powders  every  three  hours, 
how  many  powders  will  he  take  in  a  day,  if  he  sleeps  six 
hours  ?     How  many  will  he  take  in  five  days  ? 

If  a  French  coin  called  a  franc  is  worth  twenty  cents  of 
our  money,  how  many  francs  are  worth  a  dollar?  Three 
dollars  are  equal  to  how  many  francs?  Ten  dollars  are 
equal  to  how  many  francs  ? 

If  two  kinds  of  beans  worth  eight  cents  and  ten  cents  a 
quart  are  mixed,  what  will  be  the  price  of  a  quart  of  the 
mixture  ? 

How  many  bottles  will  be  required  for  nine  gallons  of 
wine,  if  it  takes  five  bottles  for  a  gallon  ? 

Forty  bottles  will  hold  how  many  gallons  of  wine  at  five 
bottles  for  a  gallon  ? 

If  a  dealer  in  gloves  buys  at  a  dollar  a  pair,  and  sells  at 
a  dollar  and  a  quarter,  how  much  does  he  gain  on  a  dozen 
pairs  of  gloves  if  one  pair  of  gloves  proves  worthless  ? 

If  children's  stockings  can  be  bought  at  twelve  and  a 
half  cents  apiece,  what  will  four  pairs  cost?  What  part 
of  a  dollar? 

How  many  legs  must  be  made  for  twenty-one  wooden 
horses  ? 


NUMBERS   FROM  SIXTY   TO  SEVENTY.  397 

There  are  fifty-two  weeks  in  a  year.  How  many  weeks 
are  in  four  years  ? 

There  are  thirty-two  quarts  in  a  bushel.  How  many 
quarts  in  three  bushels  ? 

If  a  bushel  of  potatoes  weighs  sixty  pounds,  what  will 
nine  bushels  weigh  ? 

A  man  who  had  ninety-seven  turkeys  sold  seventy-four. 
How  many  had  he  left  ? 

A  barrel  of  flour  weighs  one  hundred  and  ninety-six 
pounds.  When  sixty-four  pounds  have  been  used,  how 
many  pounds  are  left  ? 

If  there  are  eighty-seven  pages  in  your  reader,  and  you 
have  read  fifty-four  pages,  how  many  pages  have  you  still 
to  read  ? 

What  was  the  cost  of  a  man's  breakfast  if  he  paid  five 
cents  for  a  cup  of  coffee,  twelve  cents  for  fish,  and  thirty- 
two  cents  for  bread  and  meat  ? 

A  lady  doing  her  marketing  bought  a  head  of  lettuce  for 
twenty-three  cents,  some  tomatoes  for  fifteen  cents,  and 
some  beef  for  fifty  cents.     How  much  did  she  spend  ? 

A  house  three  stories  high  had  eight  windows  for  each 
story  in  front,  half  that  number  in  each  story  behind,  and 
a  fourth  of  that  number  on  each  side.  How  many  windows 
had  the  house  ? 

What  is  the  height  of  a  house  if  the  ground  floor  is  twelve 
feet  high,  the  next  floor  eleven  feet  high,  and  the  garrets 
and  roof  fifteen  feet  high  ? 

Three  times  four-sixths  are  how  many  whole  ones  ? 

Four  times  five-tenths  are  how  many  whole  ones  ? 

Three  times  six-ninths  are  how  many  whole  ones  ? 

Four  times  six-eighths  are  how  many  whole  ones  ? 

Six  times  six-ninths  are  how  many  whole  ones  ? 

Twelve  times  four-sixths  are  how  many  whole  ones  ? 


S98  FIRST  STEPS   IN  NUMBER. 

Square  Numbers. 

Draw  a  square  two  inches  on  a  side.  Divide  it  into 
square  inches.  How  many  square  inches  does  the  square 
contain  ? 

If  the  square  were  two  feet  on  a  side,  how  many  square 
feet  would  it  contain  ? 

If  the  square  were  two  yards  on  a  side,  how  many  square 
yards  would  it  contain  ? 

If  any  square  is  two  units  on  a  side,  how  many  such 
square  units  will  it  contain  ? 

Since  any  square  two  units  on  a  side  contains  four  square 
units,  we  say  the  square  of  two  is  four. 

Write  :  The  square  of  two  is  four. 

We  usually  express  it  this  short  way :  2^  =  4. 

Draw  a  square  three  inches  on  a  side,  and  find  the  num- 
ber of  square  inches  it  contains. 

Draw  a  square  three  feet  on  a  side,  and  find  how  many 
square  feet  it  contains. 

How  many  square  yards  in  a  square  that  is  three  yards 
on  a  side  ? 

If  a  square  is  three  units  on  a  side,  how  many  such 
square  units  will  it  contain  ? 

What,  then,  is  the  square  of  three  ? 

Express  it  in  this  way  :  3^  =  9. 

Who  can  think  how  many  square  inches  a  square  four 
inches  on  a  side  will  contain?  Find  out  by  drawing  a 
square  if  you  cannot  think. 

If  any  square  is  four  units  on  a  side,  how  many  such 
square  units  will  it  contain  ? 

Express  the  square  of  four.     (4^  =  16.) 

If  a  square  is  five  units  on  a  side,  how  many  square  units 
will  it  contain  ? 

Express  the  square  of  ^^q,     (5^  =  26.) 


NUMBERS   FROM  SIXTY   TO  SEVENTY.  399 

If  a  square  is  six  units  on  a  side,  how  many  square  units 
will  it  contain  ? 

Express  the  square  of  six.     (6^  =  36.) 

Express  the  square  of  seven. 

If  a  square  is  eight  inches  on  a  side,  how  many  square 
inches  will  it  contain  ? 

Express  the  square  of  eight. 

Name  the  numbers  between  one  and  twenty  that  are 
square  numbers ;  between  twenty  and  fifty.  What  other 
square  numbers  do  you  know  ? 

Odd   and    Even    Numbers. 

Name  a  number  that  will  contain  two  without  a  remain- 
der.    (4.) 

Four  is  an  even  number. 

Name  another  number  that  will  contain  two  without  a 
remainder.     (8.) 

Eight  is  an  even  number. 

Name  another  even  number. 

Name  as  many  even  numbers  as  you  can  think  of. 

Begin  with  two  and  name  them  in  order. 

Who  can  write  a  dozen  even  numbers  in  a  minute  ? 

Write  a  score  of  numbers  that  are  not  even. 

Such  numbers  are  odd. 

Name  ten  odd  numbers,  beginning  with  one. 

See  if  you  can  discover  with  what  figures  even  numbers 
must  end. 

If  even  numbers  end  with  0,  2,  4,  6,  or  8,  with  what  fig- 
ures do  odd  numbers  end  ? 

As  I  express  these  numbers  you  may  tell  me  whether 
they  are  odd  or  even :  15,  9,  18,  21,  25,  26,  30,  74,  87. 


CHAPTEE  XXXIII. 

NUMBERS  FROM  SEVENTY  TO  EIGHTY-FOUR. 


§  70.    The  Number  Seventy-Two. 

Facts  to  be  taught : 

12  X    6                  6x12 

9x    8 

Sx    9 

72^-   6                72^12 

72-f-   8 

72-^   9 

iVof72                 ^of72 

iof72 

iof72 

§  71.    The  Number  Eighty-One. 

Facts  to  be  taught : 

9x9  ^ofSl  81 -f- 9  92 

Exercise  for  Review. 

A  man  who  buys  chairs  for  twenty-four  dollars  per 
dozen  sells  them  for  thirty  dollars  per  dozen.  What  does 
he  gain  on  twelve  dozen  chairs  ? 

If  I  pay  a  cent  apiece  for  apples,  two  cents  apiece  for 
peaches,  and  three  cents  apiece  for  pears,  what  do  I  pay 
for  a  dozen  of  each  ? 

A  stationer  bought  twelve  dozen  pens  for  seventy-two 
cents,  and  sold  them  for  twelve  cents  a  dozen.  What  did 
he  gain  on  the  lot  ? 

If  a  man  saves  from  his  earnings  twelve  dollars  a  month, 
how  much  will  he  save  in  half  a  year  ? 


NUMBERS   FROM  SEVENTY   TO  EIGHTY-FOUR.       401 

If  I  earn  thirty-six  dollars  a  week,  and  save  one-sixth  of 
it,  in  how  many  weeks  shall  I  save  seventy-two  dollars  ? 

Two  ships  are  sailing  in  the  same  direction,  seventy-two 
miles  apart.  If  the  second  ship  gains  on  the  other  twelve 
miles  a  day,  in  how  many  days  will  it  overtake  the  first? 

If  the  price  of  a  mirror  is  seventy-two  dollars,  and 
one-sixth  of  the  price  is  deducted  from  it,  what  then  is 
the  price  of  the  mirror  ? 

A  man  paid  sixty-four  dollars  for  chairs  at  eight  dollars 
each,  and  sold  them  for  nine  dollars  each.  For  how  much 
did  he  sell  them  ? 

How  many  baskets  will  six  dozen  oranges  fill,  if  each 
basket  holds  eight  oranges  ? 

A  horse  travelled  seventy-two  miles  in  twelve  hours.  A 
bicycle  went  the  same  distance  in  nine  hours.  What  was 
the  difference  in  speed  per  hour  between  the  horse  and 
the  bicycle  ? 

If  a  boy  begins  school  at  five  years  old  and  goes  to 
school  nine  months  a  year  until  he  is  fourteen  years  old, 
how  many  months  schooling  will  he  have  if  he  is  out  of 
school  one  year  in  the  meantime  ? 

Eight  years  give  how  many  school  months  at  nine  school 
months  a  year  ? 

Six  dozen  rosebuds  will  be  enough  for  how  many  bou- 
quets, if  nine  are  used  for  each  bouquet  ? 

My  room  is  six  feet  between  the  ceiling  and  the  mop- 
board.  If  there  is  a  bordering  above  and  below,  each  one- 
eighth  of  this  distance  in  width,  how  many  inches  between 
the  two  borders  ? 

If  it  costs  five  cents  for  meat  and  four  cents  for  bread 
for  breakfast,  what  will  nine  breakfasts  cost  ? 

I  have  in  my  purse  three  quarters  of  a  dollar,  a  five-cent 
piece,  and  one  cent.  How  many  slates  at  nine  cents  each 
will  the  money  buy  ? 


402  FIRST  STEPS   IN   NUMBER. 

Our  pear  tree  bore  eigtty-one  pears  this  year.  If  we  eat 
one-ninth  of  the  pears  each  day,  how  many  days  will  they 
last? 

How  many  square  inches  will  a  square  nine  inches  on  a 
side  contain  ?  If  the  square  were  one  inch  less  on  a  side, 
how  many  square  inches  would  it  contain  ?  If  it  were  two 
inches  less  on  a  side,  how  many  square  inches  would  it 
contain  ? 

In  a  silk  quilt  that  I  am  making,  some  of  the  squares 
are  three  inches  on  a  side  and  some  ^ye  inches.  How 
many  more  square  inches  in  one  square  than  in  the  other  ? 

How  many  more  squares  two  inches  on  a  side  can  you 
cut  from  a  square  six  inches  on  a  side  than  from  a  square 
four  inches  on  a  side  ? 

How  many  more  squares  three  inches  on  a  side  can  you 
cut  from  a  square  nine  inches  on  a  side  than  from  one  six 
inches  on  a  side  ? 

The  square  of  nine  divided  by  the  square  of  three  is 
how  many  ?  The  square  of  eight  divided  by  the  square  of 
four  ?     The  square  of  six  divided  by  the  square  of  two  ? 

The  square  of  nine  equals  how  many  nines  ?  The  square 
of  seven  equals  how  many  sevens?  The  square  of  five 
equals  how  many  fives? 

If  my  watch  is  thirty  seconds  slow,  what  part  of  a 
minute  is  it  behind  time  ? 

If  it  is  a  thirty  minutes'  walk  to  school,  what  part  of  an 
hour  does  it  take  to  walk  to  school  ? 

What  part  of  an  hour  are  ten  minutes  ?  twenty  minutes  ? 

Where  is  the  long  hand  when  the  time  is  fifteen  minutes 
past  three?  ten  minutes  past  three?  twenty  minutes  past 
three?  half  past  three?  a  quarter  of  four?  quarter  past 
four? 

Where  are  the  hands  of  a  clock  at  four  o'clock  ?  at  eight 
o'clock  ?  at  ten  o'clock  ? 


NUMBERS   FROM  SEVENTY   TO   EIGHTY-FOUR.        403 

What  time  is  it  wlien  both  hands  point  to  twelve  ? 

What  kind  of  an  angle  is  formed  by  the  two  hands  of  a 
clock  at  three  o'clock  ?  At  what  other  hour  is  the  same 
angle  formed  ?  What  kind  of  an  angle  is  formed  at  five 
o'clock?  at  eleven  o'clock?  at  one  o'clock?  What  kind  of 
a  line  is  formed  by  the  hands  of  a  clock  at  six  o'clock  ? 

Write  in  a  line  the  numbers  that  contain  nine  without  a 
remainder  as  far  as  eighty-one,  and  see  if  you  can  discover 
anything  remarkable  about  the  numbers. 

Write  in  a  line  the  numbers  that  contain  eleven  without 
a  remainder  as  far  as  seventy-seven,  and  discover  what 
you  can  about  them. 

Write  in  a  line  the  numbers  that  contain  five  without  a 
remainder  as  far  as  eighty,  and  tell  me  what  you  can  about 
them. 

With  what  figure  does  every  number  end  that  contains 
ten  without  a  remainder  ? 

Can  you  think  of  any  odd  number  that  contains  an  even 
number  without  a  remainder  ? 

Can  you  think  of  any  odd  numbers  that  contain  odd 
numbers  without  a  remainder  ? 

Into  how  many  parts  must  you  divide  five  to  get  one 
for  each  part?  Into  how  many  parts  must  you  divide 
fourteen  to  get  two  for  each  part  ?  Into  how  many  parts 
must  you  divide  thirty  to  get  six  for  each  part  ?  forty  to 
get  five  for  each  part  ?  fifty-four  to  get  nine  for  each  part  ? 
sixty-three  to  get  seven  for  each  part?  seventy-two  to  get 
six  for  each  part  ?  to  get  twelve  for  each  part  ?  to  get  eight 
for  each  part  ?  to  get  nine  for  each  part  ? 

Two  pounds  are  how  many  ounces  ? 

Two  quires  of  paper  are  how  many  sheets  of  paper  ? 

Five  reams  of  paper  are  how  many  quires  of  paper  ? 

A  man  buys  a  stove  for  old  iron,  paying  $1.00  for  it. 
He  fits  it  up  with  a  new  grate,  a  new  door,  and  some  new 


404  FIRST  STEPS   IN   NUMBER. 

hinges,  which  cost  him  $1.00  all  together,  and  sells  the 
stove  for  $  7.00.     What  does  he  make  by  his  bargain  ? 

How  much  money  will  it  take  for  your  dictionary  at 
$2.25,  your  reader  at  $1.25,  your  geography  at  $1.38, 
your  drawing-book  at  $0.25,  your  history  at  $0.75,  and 
your  pencils  and  paper  at  $  0.45  ?     ($  6.33.) 

If  I  buy  a  barrel  of  flour  for  $7.37,  a  barrel  of  sugar  for 
$  12.75,  a  gallon  of  molasses  for  $  0.85,  a  tub  of  butter  for 
$  6.68,  some  meat  for  $0.68,  and  vegetables  for  $0.47,  what 
do  I  pay  for  the  whole  ?     ($28.80.) 

If  I  read  14  pages  in  a  book  one  day,  27  another  day,  35 
another  day,  19  another  day,  47  another  day,  17  another 
day,  and  there  are  87  more  pages  in  the  book,  how  many 
pages  does  the  book  contain  ?     (246  pages.) 

I  bought  some  dress  goods  for  $17.75,  some  lace  for 
$8.37,  some  buttons  for  $0.75,  some  dress  lining  for  $0.47, 
a  stick  of  braid  for  $  0.06,  and  some  some  sewing  silk  for 
$  0.28.     What  was  my  bill  for  the  whole  ?     ($  27.68.) 

Of  $  1.87  which  I  had  in  my  purse  I  spent  $  0.07  for  a  box 
of  elastic  bands,  $  0.25  for  two  quires  of  paper,  $0.09  for  four 
pencils,  and  $  0.27  for  a  book.    What  had  I  left  ?    ($1.19.) 

If  I  earn  $107.00  one  month  and  $125.00  another 
month,  how  much  more  do  I  earn  the  second  month  than 
the  first?     ($18.00.) 

If  there  are  181  children  on  the  upper  floor  of  a  room, 
and  157  on  the  lower  floor,  how  many  more  children  on  the 
upper  floor  than  on  the  lower  floor  ?     (24  children.) 

A  bushel  of  corn  weighs  56  pounds.  What  will  6  bush- 
els weigh?     (336  pounds.) 

A  barrel  of  flour  weighs  196  pounds.  What  will  a  load 
of  8  barrels  weigh?     (1568  pounds.) 

A  gross  of  pens  is  144  pens.  How  many  pens  in  9 
gross?     (1196  pens.) 

How  many  sheets  of  paper  in  9  quires  of  paper  ?  (216 
sheets  of  paper.) 


NUMBERS   FROM  SEVENTY  TO   EIGHTY-FOUR.        405 

How  many  ounces  in  8  pounds  ?  (128  ounces.) 
How  many  quarts  in  8  bushels?  (256  quarts.) 
In  an  orchard  there  were  6  rows  of  trees  with  13  trees  in 

each  row,  and  37  trees  around  the  outer  edge  of  the  orchard. 

If  58  of  these  trees  died,  how  many  were  left  ?     (57  trees.) 
A  man  bought  2  bushels  of  apples  at  $0.75  a  bushel,  and 

sold  them  for  $0.37  a  peck.    How  much  did  he  gain  if  one 

peck  of  apples  decayed  ?     ($1.09.) 

If  a  pound  of  flour  is  put  into  each  loaf  of  bread,  how 

many  loaves  of  bread  can  be  made  from  2  barrels  of  flour  ? 

(392  loaves.) 

The  Rod. 

Bertha  may  take  one  end  of  this  string  and  Charles  the 
other  end.  Stand  as  far  apart  as  the  length  of  the  string. 
Bertha  and  Charles  are  a  rod  apart.  How  long  then  is 
the  string  they  hold  ? 

I  have  here  several  other  strings  just  as  long.  How  long 
is  each? 

Edna  and  Mary  may  take  one,  and  mark  off  a  rod  on 
the  platform. 

Annie  and  Harry  may  take  another,  and  measure  off  a 
rod  on  the  long  blackboard. 

Sarah  and  Maggie  may  measure  off  a  rod  on  the  floor. 

The  others  may  see  if  the  measuring  is  correctly  done. 

How  long  a  distance  have  you  marked  off  in  each  case  ? 

John  may  see  how  many  of  his  steps  it  takes  to  make  a  rod. 

Clarence,  place  yourself  a  rod  from  the  door.  You  are 
two  inches  short  of  a  rod. 

Clara,  place  yourself  a  rod  from  my  table.  You  are 
right  within  half  an  inch. 

What  distance  in  the  school  yard  do  you  think  to  be  a 
rod  ?     Who  has  ever  seen  any  one  measure  with  a  rod  line  ? 

What  is  measured  by  the  rod  ? 


406  FIRST  STEPS   IN  NUMBER. 

I  will  give  each  two  of  you  a  line  wHcli  is  a  rod  long, 
and  some  time  to-day  you  may  measure  off  a  rod  in  the 
school  yard.     Place  small  sticks  to  mark  the  distance. 

Yards  in  a  Rod. 

Who  has  found  out  how  many  yards  there  are  in  the  line 
which  measures  a  rod  ? 

You  may  measure  your  rod  lines,  using  the  yard  lines 
which  I  have  drawn  on  the  board.  How  many  times  do 
you  find  the  yard  to  be  contained  in  the  rod  ?  Each  dis- 
tance then  which  you  have  measured  and  found  to  be  a  rod 
contains  how  many  yards? 

Write  :  Five  and  a  half  yards  equal  a  rod. 

Two  rods  equal  how  many  yards?  three  rods?  seven 
rods  ?  ten  rods  ?  twelve  rods  ? 

A  rod  equals  how  many  feet  ? 

Rods  in  a  Mile. 

If  I  ask  how  far  it  is  to  the  next  town,  will  the  distance 
be  given  me  in  inches  ?  Will  it  be  given  me  in  feet  ?  in 
yards  ?  in  rods  ?     In  what  will  the  distance  be  given  me  ? 

John  is  right  when  he  says  the  distance  will  be  given  me 
in  miles. 

Name  a  point  that  is  a  mile  from  here ;  that  is  two 
miles ;  that  is  several  miles. 

Name  any  two  points  you  know  that  are  a  mile  apart. 

What  is  the  longest  distance  in  miles  that  you  have 
walked  at  one  time  ? 

How  many  miles  do  you  think  all  the  steps  that  you  take 
in  a  day  would  make  ?  If  you  should  carry  in  your  pocket 
a  little  instrument  called  a  pedometer,  it  would  mark  the 
number  of  steps  you  take,  and,  if  you  know  the  length  of  your 
step,  can  you  find  how  far  you  have  walked  during  the 
day  ?     If,  for  example,  you  walk  ninety-eight  steps,  and 


NUMBERS   FROM  SEVENTY   TO   EIGHTY-FOUR.        407 

your  step  is  two  feet,  how  many  feet  do  you  walk  ?  If  you 
take  one  hundred  and  fifty  steps,  how  many  feet  do  you 
walk?  If  you  take  eight  steps  in  walking  a  rod,  how 
many  rods  do  you  walk  in  taking  seventy-two  steps  ? 

If  you  should  walk  tho^ee  hundred  and  twenty  rods,  you 
would  walk  a  mile.  If  you  walk  two  miles,  how  many 
rods  do  you  walk  ?  three  miles  ?  six  miles  ?  seven  miles  ? 

If  you  take  eight  steps  in  walking  a  rod,  how  many  steps 
will  you  take  in  walking  a  mile  ? 

If  you  can  walk  a  rod  in  three  seconds  of  time,  how  many 
seconds  will  it  take  you  to  walk  a  mile  ? 

Write  :  Three  hundred  and  twenty  rods  equal  a  mile. 

What  is  the  name  of  the  shortest  distance  you  know  ? 
of  the  next  longer  distance  ?  of  the  next  longer  distance  ? 
of  the  next  longer  distance?  of  the  longest  distance  ? 

Write  in  a  table  the  number  it  takes  of  each  of  these 
distances  to  equal  one  of  the  next  higher. 

You  have  written  the  Table  of  Long  Measure. 

Read  the  table  of  long  measure. 

Roman  Numerals. 

You  may  express  one  on  the  board  in  all  the  ways  you 
can.     (1,  one,  |.) 

If  you  look  at  the  clock,  you  will  see  another  way. 

What  other  letters  are  used  to  express  numbers  on  the 
clock? 

There  are  four  other  letters  used  to  express  numbers : 
L,  0,  D,  M.  How  many  letters  are  used  to  express  num- 
bers ?     Name  them.     Write  them  in  their  order. 

A  people,  called  the  Romans,  first  used  these  letters  to 
express  numbers,  so  we  call  them  the  Roman  Numerals. 

Express  one  with  a  Roman  numeral. 

Look  at  the  clock,  and  then  express  fiYe  with  a  Roman 
numeral.     Express  ten  with  a  Roman  numeral. 


408  FIRST  STEPS   IN   NUMBER. 

I  will  express  fifty  with  a  Roman  numeral  (L  =  60). 

What  letter  expresses  fifty  ? 

What  letter  expresses  one  ? 

What  letter  expresses  five  ? 

What  letter  expresses  ten  ? 

What  letter  expresses  fifty  ? 

What  number  does  I  express  ? 

What  number  does  V  express  ? 

What  number  does  X  express  ? 

What  number  does  L  express  ? 

0  stands  for  one  hundred. 

Express  one  hundred  with  a  Roman  numeral. 

Look  at  the  figures  I  have  written  on  the  board.  (1,  5, 
10,  50,  100.)  As  I  touch  each,  tell  me  the  letter  to  write 
for  it  ? 

What  letter  comes  next  ?     (D.) 

D  stands  for  five  hundred. 

Express  five  hundred  with  a  Roman  numeral.     (D  =  500.) 

The  remaining  letter  expresses  one  thousand. 

Write  :  M  stands  for  one  thousand.     (M  =  1000.) 

Name  the  letters  that  are  used  to  express  numbers. 
What  are  they  called  ? 

Copy  and  learn :  I-l;  V-5;  X  =  10;  L-50; 
C  -  100 ;    D  -  500  ;    M  =  1000. 

Combination  of  Roman  Numerals  to  form  Other 
Numbers. 

What  value  does  I  denote  ? 

What  value  does  V  denote  ? 

Of  these  two  letters,  I  and  V,  place  the  one  denoting  the 
less  value  before  the  other. 

Read  what  you  have  written  (IV). 

Subtract  the  value  of  the  less  from  the  greater,  and  you 
will  have  the  number  for  which  IV  stands. 


NUMBERS   FROM  SEVENTY   TO   EIGHTY-FOUR.        409 

This  is  one  way  the  Romans  used  to  make  up  their  numbers. 

What  value  does  X  denote  ? 

Of  these  two  letters,  I  and  X,  place  the  one  denoting  the 
less  value  before  the  other. 

Read  what  you  have  written  (IX). 

Subtract  the  less  from  the  greater,  and  you  will  find  what 
IX  stands  for. 

What  value  does  L  denote  ? 

Of  these  two  letters,  X  and  L,  place  the  one  denoting 
the  less  value  before  the  other. 

Read  what  you  have  written  (XL). 

Subtract  the  value  of  the  less  from  the  greater,  and  you 
will  find  what  XL  stands  for. 

What  does  XC  stand  for? 

As  I  point  to  these  Roman  numerals,  you  may  name  the 
value  which  they  express  :  I,  IV,  V,  X,  L,  C,  D,  M,  IV, 
IX,  XL,  XC,  IX,  L,  XL,  C,  XC. 

What  four  new  numbers  have  you  made  to-day  with  the 
Roman  numerals?     (4,  9,  40,  90.) 

What  stands  for  four  ?  What  stands  for  forty  ? 

What  istands  for  nine  ?  What  stands  for  ninety  ? 

When  I  stands  before  V,  what  do  you  do  to  find  the  value 
of  IV? 

When  I  stands  before  X,  what  do  you  do  ? 

When  X  stands  before  L,  what  do  you  do  ? 

When  X  stands  before  C,  what  do  you  do  ? 

What  Roman  numeral  stands  for  one  ? 

Who  knows  what  stands  for  two  ?  for  three  ? 

If  two  I's  stand  for  two,  what  should  you  think  two  X's 
would  stand  for  ?  three  X's  ? 

Since  two  X's  stand  for  twenty,  what  should  you  think 
two  C's  would  stand  for?  three  C's?  four  C's?  two  M's  ? 
three  M's? 

Name  the  number  as  I  show  you  the  Roman  numerals: 


410  FIRST   STEPS   IN   NUMBER. 

II,  III,  IV,  V,  IX,  X,  XX,  XXX,  XL,  L,  XC,  C,  CC,  CCC, 
CCCC,  D,  M,  IV,  IX,  XL,  XC,  XX,  XXX,  CC,  CCC. 

You  may  write  these  numbers  iu  Roman  numerals  :  1,  2, 
3,  4,  5,  9,  10,  20,  30,  40,  50,  90,  100,  200,  300,  400. 

When  two  letters  of  the  same  value  stand  together,  what 
do  you  do  to  find  the  value  exprevssed  ? 

How  many  ways  have  you  found  that  the  Romans  put 
letters  together  to  make  numbers  ? 

If  you  look  at  the  clock,  you  will  find  how  six  is  made. 
What  forms  six  ?  But  wdiere  does  the  less  number  stand 
with  reference  to  the  greater  ?  And  what  do  you  do  to  the 
two  numbers  to  find  six?  What  other  numbers  on  the 
clock  are  made  in  the  same  way  ? 

Who  knows  any  other  numbers  made  in  the  same  way  ? 
All  numbers  that  you  have  not  already  learned  to  ex- 
press in  Roman  numerals  are  made  in  this  way. 

See  if  you  can  expi'css  the  numbers  between  twelve  and 
twenty  ;  between  twenty  and  thirty  ;  between  thirty  and 
forty  ;  between  forty  and  fifty. 

Add  and  express  the  sum  in  Roman  numerals  : 
Five,  seven,  six,  nine,  eight,  six. 
Twelve,  eight,  nineteen,  three,  seven,  one. 
Three,  eight,  seven,  five,  eight,  six. 
Four,  nine,  thirteen,  three. 
Two,  seven,  six,  four. 

Seven,  eight,  ten,  twenty-five,  eleven,  eight. 
Eight,  nine,  seventeen,  eight,  twenty,  nine. 
AVrite  in  Roman  numerals  the  odd  numbers  to  twelve. 
Ex^^ress  all  the  numbers  you  can,  using  but  one  letter 
for  each  number. 

Express  all  the  numbers  you  can,  using  but  two  letters 
for  each  number. 

Express  the  products  of  ten  as  far  as  one  hundred  in 
Roman  numerals. 


CHAPTER  XXXIV. 

NUMBERS  FROM  EIGHTY-FOUR  TO  ONE   HUNDRED. 


§  72.   The  Number  Eighty-Four. 
Facts  to  be  taught : 


12  X    7 

7x12               ^of84 

84-^   7 

84-f-12               iof84 

Wof84 

|of84                2x42 

§  73.    The  Number  Ninety-Six. 

Facts  to  be  taught : 

12  X    8 

.8x12               iof96 

96--   8 

96  ■+- 12               3  X  32 

A  of  96 

iof96               2x48 

Exercise  for  Revie\v. 

Nellie  is  9  years  old,  and  Annie  is  16.  What  is  the  dif- 
ference of  their  ages  in  months  ? 

In  a  dozen  weeks  how  many  days  ? 

If  I  pay  for  room  rent  $7.00  a  month,  what  is  my  rent 
for  a  year  ? 

A  man  made  a  fence  across  a  garden  that  is  12  yards 
wide.  If  he  put  in  posts  2  yards  apart  to  support  the 
railing,  how  many  posts  dii  he  use,  providing  there  was 
a  post  at  each  end  ?  How  many  posts  would  be  required 
for  12  fences  the  same  length  ?  If  the  fence  formed  one 
straight  line,  but  12  times  as  long  as  the  fence  across  the 
garden,  would  84  posts  be  required  ?     Why  ? 


412  FIRST   STEPS   IN  NUMBER. 

A  grocer  paid  f  0.84  for  figs  at  |0.07  a  pound.  He  lost 
two  pounds  by  drying  and  by  bad  figs.  If  he  sold  the  rest 
at  $0.10  a  pound,  what  did  he  gain  on  the  whole? 

How  many  times  does  the  short  hand  go  round  the  dial 
in.  84  hours  ? 

While  the  short  hand  is  going  round  the  dial  7  times, 
how  many  times  does  the  long  hand  go  round  the  dial  ? 

How  many  times  does  the  short  hand  go  round  the  dial 
in  a  day  ?     How  many  times  will  it  go  round  in  42  days  ? 

How  broad  is  a  lake  which  is  42  feet  half-way  over  ? 

If  $0.12  is  a  seventh  of  the  price  of  a  book,  what  is  the 
price  of  the  book  ? 

A  strip  of  ribbon  84  yards  in  length  was  cut  into  7  equal 
pieces.  How  many  yards  were  in  each  piece  ?  If  the  rib- 
bon was  sold,  at  $0.84  a  piece,  what  was  the  price  per 
yard? 

If  a  merchant  sells  21  yards  of  silk  for  a  dress,  how 
many  yards  are  in  a  piece  of  goods  from  which  he  can  sell 
4  dresses? 

What  four  equal  numbers  make  84  ?  What,  then,  is 
one-fourth  of  84? 

If  there  are  84  windows  in  a  building,  and  one-fourth  of 
this  number  is  in  the  front  of  the  building,  how  many  win- 
dows are  on  the  two  sides  and  at  the  back  ? 

If  $0.84  will  buy  12  car-tickets,  what  is  the  price  of 
one  car-ticket  ? 

A  man  charged  $0.84  a  yard  for  carpeting,  but  at  length 
agreed  to  deduct  one-twelfth  of  that  price.  What,  then, 
was  his  price  for  the  carpeting  ?  How  much  less  did  12 
yards  cost  than  if  the  first  grice  had  been  paid?  How 
many  yards  of  carpet  lining  would  that  buy  at  $0.07  a  yard? 

If  a  peck  of  berries  cost  $0.96,  what  is  that  a  quart? 

Into  how  many  piles  can  I  separate  96  oranges,  if  I  put 
a  dozen  in  each  pile  ? 


NUMBERS   FROM   EIGHTY-FOUR  TO  ONE   HUNDRED.    413 

A  man  has  4  baskets,  each  containing  24  apples.  If 
he  sells  them  at  $0.05  a  dozen,  what  will  he  receive? 

A  man  had  96  books.  He  sold  84  books.  What  part 
of  the  whole  number  had  he  left  ? 

A  man  shipped  eight  dozen  boxes  of  oranges  from  Flor- 
ida. When  the  oranges  arrived,  -^  was  found  to  have 
decayed.     How  many  boxes  were  good  ? 

A  train  travels  ninety-six  miles  in  three  hours.  What 
is  the  rate  of  speed  per  hour  ? 

A  man  bought  a  bushel  of  peaches  at  |0.03  a  quart. 
What  did  he  pay  for  the  bushel  of  peaches  ? 

If  a  large  cask  holds  48  gallons,  what  will  2  casks  hold  ? 

A  man  works  96  hours  in  a  week  and  two  days.  How 
many  hours  a  day  does  he  work  ? 

If  a  pencil  costs  $0.05  and  an  eraser  costs  $0.03,  what 
will  a  dozen  of  each  cost  together  ?  How  many  cents  less 
than  a  dollar  ? 

At  $0.08  a  card,  how  many  cards  can  I  buy  for  $0.96  ? 

Charles  gets  $6.00  a  month  for  helping  his  father. 
Emma  gets  \  as  much  for  helping  her  mother.  How  much 
will  both  have  earned  in  a  year  ? 

How  broad  is  a  house  which  is  3  rooms  in  breadth,  each 
room  being  15  feet  broad,  the  two  outer  walls  being  each  2 
feet  thick,  and  the  partitions  between  the  rooms  each  ^  a 
foot  thick  ? 

How  many  rods  are  there  in  3  miles  ? 

How  many  hours  are  there  in  a  week? 

If  an  orange  is  worth  3  apples,  how  many  apples  are  a 
dozen  oranges  worth?  How  many  oranges  are  a  dozen 
apples  worth  ? 

How  far  is  it  around  a  square  which  is  19  feet  on  a  side  ? 

If  one  scale  pan  had  25  pounds  in  it,  and  the  other  had 
13  pounds  in  it,  how  many  pounds  must  be  taken  from  one 
and  put  into  the  other  to  make  the  scales  balance  ? 


414  FIRST   STEPS    IN   NUMBER. 

Into  how  many  bunches,  containing  5  bananas  each,  can 
you  separate  a  bunch  of  40  bananas  ?  a  bunch  of  60  bana- 
nas ?  a  bunch  of  30  bananas  ? 

If  you  use  a  drop  of  ink  at  2  dips,  how  many  dips  can 
you  take  from  a  bottle  containing  125  drops,  if  15  drops 
dry  up  ? 

If  I  packed  84  pairs  of  shoes  in  4  boxes,  putting  an  equal 
number  of  pairs  in  each  box,  how  many  pairs  did  I  put  in 
each  box  ? 

A  man  had  a  dozen  boxes  of  candy,  and  8  pounds  in 
each  box.  If  he  put  this  candy  up  in  packages  containing 
a  quarter  of  a  pound  each,  how  many  packages  will  he 
have? 

If  while  you  were  pumping  20  gallons  of  water  out  of  a 
well,  one  gallon  ran  in,  how  many  gallons  less  were  there 
in  the  well  after  you  pumped  the  water  than  before  ? 

If  each  one  of  a  family  of  8  persons  use  2  gallons  of 
water  in  a  day,  how  much  will  they  use  in  a  week  ? 

A  quire  of  paper  will  make  how  many  strips  of  paper,  if 
each  sheet  is  cut  into  four  strips  ? 

If  I  start  from  my  home  and  travel  4  miles  in  one  direc- 
tion, and  then  turn  about  and  travel  5  miles  from  my  home 
in  the  opposite  direction,  how  many  miles  do  I  travel  be- 
fore I  reach  home  ? 

If  I  go  to  West  Kock,  which  is  3  miles  from  my  home, 
and  then  to  East  Kock,  which  is  5  miles  from  my  home  in 
the  opposite  direction,  how  far  do  I  travel  before  I  reach 
home? 

A  river  at  low  water  was  200  feet  wide,  but  at  high 
water  it  spread  over  the  shore  on  one  side  25  feet,  and  on 
the  other  side  38  feet.  How  wide  was  the  river  at  high 
water  ? 

What  will  4  dozen  plates,  at  $1.87  a  dozen,  and  6  dozen 
saucers,  at  $  0.98  a  dozen,  cost  ? 


NUMBERS  FROM   EIGHTY-FOUR  TO  ONE   HUNDRED.      415 

Whicli  is  the  cheaper,  boots  at  $  3.00  a  pair,  if  I  wear 
out  4  pairs  in  a  year,  or  boots  at  $8.00  a  pair,  if  I  wear  out 
3  pairs  in  two  years  ? 

If  you  have  a  half  a  dollar,  how  many  quarters  of  a 
dollar  is  it  worth?  how  many  eighths  of  a  dollar? 

If  you  have  a  half  of  a  quire  of  paper,  how  many  sixths 
of  a  quire  have  you  ?  how  many  twelfths  of  a  quire  ? 

If  Jennie  is  ^  a  score  of  years  old,  and  her  brother  is  ^^ 
of  a  score  of  years  old,  how  many  times  as  old  as  her 
brother  is  Jennie? 

If  it  takes  -|-  of  a  yard  of  ribbon  for  a  loop,  how  many 
loops  will  -I"  of  a  yard  of  ribbon  make  ? 

It  is  required  to  cut  a  loaf  of  cake  into  ninths.  It  is 
already  cut  into  thirds.  Into  how  many  pieces  must  I  cut 
each  third  to  cut  the  whole  into  ninths  ? 

If  you  sleep  ^  of  the  day,  how  many  twelfths  of  the  day 
do  you  sleep? 

^  equals  how  many  fourths?  equals  how  many  sixths? 
equals  how  many  eighths  ?  equals  how  many  tenths  ?  equals 
how  many  twelfths  ? 

^  equals  how  many  sixths  ?  equals  how  many  ninths  ? 
equals  how  many  twelfths  ? 

\  equals  how  many  eighths  ?  equals  how  many  twelfths  ? 

^  equals  how  many  tenths  ? 

■^  equals  how  many  twelfths  ? 

f  equal  how  many  ones  ? 

f  equal  how  many  ones  ? 

|-  equal  how  many  ones  ? 

How  many  fifths  in  a  whole  ? 

How  many  sixths  in  a  whole  ? 

How  many  sevenths  in  a  whole  ? 

In  3  oranges  how  many  halves  ? 

In  4  dollars  how  many  fourths  ? 

In  2  yards  of  ribbon  how  many  sixths  ? 


416  FIRST  STEPS   IN   NUMBER. 

In  5  pounds  how  many  thirds  of  a  pound  ? 

In  2  dollars  how  many  fifths  of  a  dollar  ? 

In  3  yards  how  many  sevenths  of  a  yard  ? 

In  4  bushels  how  many  eighths  of  a  bushel  ? 

If  you  have  f  of  a  dollar  and  I  have  |-,  how  many  fifths 
have  we  together  ? 

If  a  grocer  has  |-  of  a  bushel  of  beans  of  one  kind,  and  f 
of  a  bushel  of  another  kind,  how  many  eighths  has  he  of 
both  kinds? 

If  a  salesman  sells  -|-  of  a  yard  of  ribbon  to  one  person, 
I  to  another,  and  -|  to  another,  how  many  sixths  does  he 
sell  all  together  ? 

If  there  is  ^  of  a  yard  of  ribbon  in  one  piece  and  ^  of  a 
yard  in  another  piece,  how  many  fourths  of  a  yard  are  in 
the  two  pieces  together  ? 

If  I  buy  ^  a  pound  of  one  kind  of  dates  and  I-  of  a  pound 
of  another  kind,  how  many  eighths  of  a  pound  do  I  buy 
in  all? 

If  I  have  ^  of  a  yard  of  velvet  and  I-  of  a  yard,  how 
many  sixths  of  a  yard  do  I  have  ? 

If  it  is  "I"  of  a  mile  to  the  post-office  and  -^q  of  a  mile  farther 
to  the  depot,  how  many  tenths  of  a  mile  is  it  to  the  depot  ? 

I  have  "I"  of  a  quire  of  letter  paper  and  -^^  ^^  ^  quire  of 
note  paper.  How  many  twelfths  of  a  quire  of  paper  have 
I  all  together  ? 

If  John  gathers  -J-  of  a  bushel  of  walnuts  and  ^  of  a  bushel 
of  chestnuts,  how  many  eighths  of  a  bushel  does  he  gather 
of  both  kinds  ? 

If  a  small  corner  of  our  yard  is  ^  of  a  rod  on  one  side 
and  ^2  0^  ^  ^^^  0^  ^^®  other  side,  how  many  twelfths  of  a 
rod  is  it  on  both  sides  ? 

If  it  is  "I-  of  a  mile  to  Walnut  Hill  and  -^  of  a  mile  up  the 
hill,  how  many  sixths  of  a  mile  is  it  from  here  to  the  top  of 
the  hill? 


NUMBERS  FROM  EIGHTY-FOUR  TO  ONE  HUNDRED.    417 

If  the  dado  of  a  room  is  ^  of  the  height  of  the  room,  and 
the  border  at  the  top  of  the  room  is  ^  of  its  height,  how  many 
ninths  of  the  height  of  the  room  are  both  dado  and  border? 

If  I  find  -|-  of  a  dozen  of  eggs  in  one  nest  and  -^  of  a 
dozen  in  another  nest,  how  many  twelfths  of  a  dozen  of 
eggs  do  I  find  in  both  nests  ? 

If  you  have  -5-  of  a  dollar  and  I  have  y^-g-  of  a  dollar,  how 
many  tenths  have  we  together? 

If  you  are  in  school  ^  of  the  day  and  study  at  home  ^ 
of  the  day,  how  many  twelfths  of  the  day  do  you  give  to 
school  work  ? 

Fred  had  50  dollars,  and  spent  ^  of  it  for  a  watch,  and 
-5^  of  it  for  a  pair  of  shoes.  How  many  tenths  of  it  did  he 
spend  ? 

A  grocer  sold  ^  of  a  bushel  of  pears  to  one  customer,  ^  to 
another,  and  -^  to  another.  How  many  sixteenths  of  a 
bushel  did  he  sell  ? 

John  spent  f  of  a  dollar  for  a  book,  ^  of  a  dollar  for 
half  a  ream  of  paper,  and  had  I-  of  a  dollar  left.  How 
much  money  had  he  at  first  ? 

James  paid  2^  dollars  for  a  hat,  3^  dollars  for  a  vest, 
and  10^  dollars  for  a  coat.     What  did  the  whole  cost  ? 

Edgar  can  do  a  certain  piece  of  work  in  3  days,  and 
Greorge  can  do  the  same  work  in  6  days.  What  part  of  the 
work  can  Edgar  do  in  1  day  ?  What  part  of  the  work  can 
George  do  in  1  day.  What  part  of  the  work  can  both  to- 
gether do  in  1  day  ? 

A  grocer  sold  ^  of  a  dozen  of  oranges  to  one  man,  -J-  of  a 
dozen  to  another,  and  -f-  of  a  dozen  to  another,  and  had  2 
dozen  left.     How  many  oranges  had  he  at  first? 

How  many  yards  is  it  half-way  round  a  flower-bed  which 
measures  18  feet  on  each  side,  and  12  feet  on  each  end  ? 


CHAPTEE   XXXV. 

PROCESSES  IN  WRITTEN  ARITHMETIC  CONTINUED. 


§  74.     Third  Step  in  Multiplication. 

Wlien  the  multiplier  consists  of  two  figures  and  the  left 
hand  figure  is  1.         • 

I  have  14  boxes  with  three  dozen  eggs  in  each  box.  I 
want  you  to  find  how  many  eggs  I  have.  Express  the 
example  on  the  board.  You  may  first  find  how  many  eggs 
I  have  in  4  boxes.  How  many  more  boxes  have  I  ?  Find 
then  how  many  eggs  I  have  in  10  boxes. 

How  many  eggs  in  4  boxes?     (144.) 

How  many  eggs  in  10  boxes?     (360.) 

How  many  eggs  in  14  boxes  ? 

Then  14  times  36  are  how  many  ? 

Frank  earned  $0.75  a  day.  How  much  did  he  earn  in 
13  days  ?  Find  first  how  much  he  earned  in  3  days  ; 
then  how  much  he  earned  in  10  days ;  and  at  last  how 
much  he  earned  in  the  whole  time. 

In  16  bushels  how  many  quarts  ?  First  find  how  many 
quarts  in  6  bushels ;  next,  how  many  quarts  in  10  bushels, 
and  then  how  many  quarts  in  16  bushels. 

If  a  bushel  of  corn  meal  weighs  56  pounds,  how  many 
pounds  will  a  bin  which  holds  15  bushels  contain?  What 
shall  we  do  first  ?  (Find  how  many  pounds  in  a  bin  which 
holds  5  bushels.)  What  next?  (Find  how  many  pounds 
in  a  bin  which  holds  10  bushels.)  What  next?  (Add,  to 
find  how  many  pounds  in  15  bushels.) 


PROCESSES   IN   WRITTEN   ARITHMETIC  CONTINUED.    419 

An  engineer  rides  97  miles  in  a  day.  How  many  miles 
does  he  ride  in  three  weeks  if  his  train  does  not  run  Sun- 
days ?  What  shall  we  do  first  ?  (Find  how  far  he  rides  in 
8  days.)  What  next  ?  (Find  how  far  he  rides  in  10  days.) 
What  last?     (Add,  to  find  how  far  he  rides  in  18  days.) 

A  merchant  sold  in  one  month  17  silk  cloaks  at  $17 
each.     What  did  he  receive  for  all  of  them  together  ? 

If  I  have  a  square  that  is  18  feet  on  a  side,  how  many 
square  feet  are  there  in  the  square  ? 

Note.  —  In  a  short  time  the  child  discovers  that  he  can  multiply 
by  units  of  tens  as  easily  as  by  single  units,  always  remembering 
that  the  first  product  is  tens.  When  he  arrives  at  this  knowledge  he 
can  multiply  by  any  number  of  tens,  and  is  ready  to  pass  to  the  next 
step  in  multiplication. 

Further  steps  in  Multiplication. 

36  364  225  367 

47  47  247  105 


-— 

360 

64 

64 

64 

105 

10 

100 

1000 

64 

64 

64 

6400 

30 

300 

3000 

3000 

Multiplications  that  can  be  Performed  by  Short 
Methods. 

1.  Multiplication  by  9. 

Annex  a  cipher,  and  subtract  the  number  to  be  multi- 
plied. 

2.  Multiplication  by  11. 

Place  the  sum  of  the  digits  between  the  digits. 

3.  Multiplication  by  25. 

Annex  two  ciphers,  and  divide  by  four. 


420  FIRST  STEPS   IN   NUMBER. 

4.  Finding  the  square  of  a  number  whose  units'  figure 
is  5. 

Multiply  the  tens  by  the  next  higher  number  of  tens, 
and  add  the  square  of  5. 

5.  Multiplication  of  two  numbers  whose  units  are  five 
and  the  difference  of  whose  tens  is  1. 

Square  the  highest  number  of  tens,  and  from  the  result 
subtract  the  square  of  5. 

6.  Multiplication  of  two  numbers  the  sum  of  whose  units 
is  ten,  and  the  difference  of  whose  tens  is  one. 

Square  the  highest  number  of  tens,  and  from  the  product 
subtract  the  square  of  the  units  of  the  highest  number. 

§  75.     First  Step  in  Division. 

When  the  dividend  is  a  multiple  of  ten,  and  the  number 
of  tens  is  a  multiple  of  the  divisor,  and  the  divisor  is  a 
number  of  units. 

Which  is  more,  two  tens  or  ten  twos  ? 

Which  is  more,  six  tens  or  ten  sixes? 

Which  is  more,  four  tens  or  ten  fours  ? 

Which  is  more,  seven  tens  or  ten  sevens? 

Which  is  more,  nine  tens  or  ten  nines  ? 

Two  tens  equal  how  many  twos? 

Three  tens  equal  how  many  threes  ? 

Four  tens  equal  how  many  fours  ? 

Six  tens  equal  how  many  sixes  ? 

Eight  tens  equal  how  many  eights? 

Nine  tens  equal  how  many  nines? 

Each  take  this  number  of  splints.  (60.)  How  many  two- 
tens  have  you  ?  Since  two  tens  and  ten  twos  are  the  same, 
three  two-tens  are  how  many  ten-twos  ?   (Three  ten-twos.) 

How  many  three-tens  do  you  find  in  60?  Then  how 
many  ten-threes  ?     (Two  ten-threes.) 


PROCESSES   IN  WRITTEN  ARITHMETIC  CONTINUED.      421 

How  many  six-tens  do  you  find  ? 

How  many  ten-sixes  then  ? 

Take  120  splints.  How  many  two-tens  in  120  ?  How 
many  ten- twos? 

How  many  three-tens  in  120  ?     How  many  ten-threes  ? 

How  many  six-tens  in  120  ?     How  many  ten-sixes  ? 

Take  90  splints.  How  many  three-tens  in  90  ?  How 
many  ten-threes  ? 

Take  140  splints.  How  many  two-tens  in  140?  How 
many  ten-twos?  How  many  seven-tens  in  140?  How 
many  ten-sevens  ? 

How  many  ten-twos  in  80?*  How  many  ten-fours  in 
80? 

How  many  ten- twos  in  100?  How  many  ten-fives  in 
100? 

How  many  ten-twos  in  160?  How  many  ten-fours  in 
160  ?     How  many  ten-eights  in  160  ? 

How  many  ten-twos  in  40  ?  Two  (times)  ten-two^  are 
how  many  twos?     Then  how  many  twos  in  40? 

How  many  ten-twos  in  60  ? 

Three  (times)  ten-twos  are  how  many  twos?  Then  how 
many  twos  in  60  ? 

See  if  you  can  find  how  many  twos  in  80.  Find  the  ten- 
twos  first,  and  then  you  can  tell  how  many  twos. 

Find  how  many  twos  in  100.  How  many  twos  in  120  ? 
How  many  twos  in  140  ? 

Find  how  many  threes  in  60.  First  find  how  many  ten- 
threes,  and  you  can  tell  how  many  threes. 

Find  the  number  of  threes  in  90  ;  in  120  ;  in  150. 

Find  the  number  of  fours  in  80  ;  in  120;  in  160. 

Find  the  number  of  fives  in  100  ;  in  150. 

Find  the  number  of  sixes  in  120 ;  in  180. 

*  Use  splints. 


422  FIRST  STEPS   IN   NUMBER. 

Find  the  number  of  sevens  in  140. 

Find  the  number  of  eights  in  160. 

Find  the  number  of  nines  in  180. 

Express  pn  the  board,  forty  divided  by  two  ;  eighty 
divided  by  two ;  one  hundred  divided  by  two ;  one  hun- 
dred and  twenty  divided  by  two;  one  hundred  and  forty 
divided  by  two. 

Express,  sixty  divided  by  three ;  ninety  divided  by 
three  ;  one  hundred  and  twenty  divided  by  three ;  one 
hundred  and  fifty  divided  by  three ;  eighty  divided  by 
four ;  one  hundred  and  twenty  divided  by  four ;  one 
hundred  and  fifty  divided  by  five  ;  one  hundred  and  eighty 
divided  by  six ;  one  hundred  and  forty  divided  by  seven ; 
one  hundred  and  sixty  divided  by  eight ;  one  hundred  and 
eighty  divided  by  nine. 

§  76.   Second  Step  in  Division. 

When  each  order  in  the  dividend  is  exactly  divisible  hy 
the  divisor. 

You  may  express  the  division  of  forty-four  by  two. 

How  many  twos  in  forty  ? 

How  many  twos  in  four  ? 

Then  how  many  twos  in  forty-four  ? 

Express  the  division  of  sixty-nine  by  three. 

How  many  threes  in  sixty  ? 

How  many  threes  in  nine  ? 

Then  how  many  threes  in  sixty-nine  ? 

Express  the  division  of  eighty-eight  by  four. 

How  many  fpurs  in  eighty  ? 

How  many  fours  in  eight? 

Then  how  many  fours  in  eighty-eight  ? 

Divide  sixty-four  by  two. 

Divide  forty-four  by  two. 


PROCESSES   IN   WRITTEN   ARITHMETIC  CONTINUED.      423 

Divide  sixty-six  by  three. 

Divide  ninety-three  by  three. 

Divide  ninety-six  by  three. 

Divide  ninety-nine  by  three. 

Divide  one  hundred  and  twenty-six  by  three. 

Divide  one  hundred  and  twenty-nine  by  three  ;  fifty-five 
by  five ;  one  hundred  and  ^ye  by  five ;  one  hundred  and 
twenty-six  by  six. 

Further  steps  in  division : 

6)96  3)37  4)136 

8)240      2)402       7)721 
13)57(      13)  152  (     13)  141  ( 

Exercise  for  Review. 

A  boy  picked  from  one  vine  enough  grapes  to  fill  a  bushel 
measure,  a  half-bushel  measure,  and  a  peck  measure.  How 
many  pecks  of  grapes  did  he  pick  ?  If  he  sells  the  grapes 
at  $0.07  a  quart,  what  does  he  get  for  a  peck  ?  If  he  had 
sold  the  grapes  for  $0.06  less  per  peck,  what  would  he 
have  received  for  the  whole  lot  ?  By  selling  his  grapes  at 
$0.50  a  peck,  how  much  less  money  would  he  get  for  the 
whole  than  by  selling  them  at  $0.07  a  quart? 

How  much  oil  do  we  use  in  8  weeks  if  we  use  a  quart 
each  evening? 

If  you  put  a  bushel  of  corn,  which  weighs  56  pounds, 
into  8  baskets,  each  holding  the  same  amount,  how  many 
pounds  of  corn  will  each  basket  contain  ? 

A  man  puts  56  quarts  of  milk  into  cans  holding  8  quarts 
each,  but  does  not  fill  the  cans  within  a  quart  each.  How 
many  more  cans  will  he  use  than  if  he  filled  each  can  ? 


424  FIRST  STEPS   IN   NUMBER. 

A  man  who  carried  56  eggs  to  market  found  -|-  of  the 
number  broken  when  he  unpacked  them.  If  eggs  were 
selling  for  $0.03  each,  how  much  did  he  lose? 

If  you  earn  $56.00  in  7  weeks,  what  is  that  per  week? 

If  Robert  found  9  hens'  nests  with  a  half  dozen  eggs  in 
each  nest,  and  left  one  egg  in  each  nest  for  the  nest-egg, 
how  many  eggs  did  he  take  away? 

How  many  square  inches  in  a  square  7  inches  on  a  side  ? 

How  many  inches  wide  is  the  window  of  a  conservatory 
for  flowers  if  there  are  9  panes  of  glass  across  it,  each  a  half 
foot  in  length,  and  the  bars  take  up  six  inches? 

In  9  pecks  of  beans  how  many  quarts  of  beans,  if  they 
shrink  in  drying  one  quart  to  a  peck? 

A  man  gave  his  note  payable  in  60  days.  How  many 
weeks  was  the  note  to  run  if  he  was  allowed  3  more  days  ? 

A  stationer  bought  12  dozen  pens  at  $0.05  a  dozen,  and 
sold  them  two  for  a  cent.     What  did  he  gain  ? 

In  -J-  of  an  hour  how  many  minutes  ? 

If  the  horse-cars  going  the  same  way  pass  my  house  five 
times  an  hour,  how  often  do  they  run  ?  If  they  pass 
twelve  times  an  hour,  how  often  do  they  run  ? 

If  in  going  in  one  direction  the  cars  pass  every  half 
hour,  how  often  do  they  pass  in  going  both  directions  ? 

If  it  takes  a  car  twenty  minutes  to  make  a  trip,  and  the 
cars  pass  each  other  half  way  on  the  trip,  how  often  do  the 
cars  pass  each  other  ?  If  the  two  cars  start  at  opposite  ends 
of  the  route  at  the  hour,  at  twenty  minutes  past  the  hour, 
and  at  twenty  minutes  of  the  hour,  at  what  times  through 
the  day  do  they  meet  ? 

If  a  trip  in  the  cars  is  9  minutes  long,  how  many  minutes 
does  it  take  the  cars  to  make  8  trips  ?  How  many  minutes 
over  an  hour  ? 

If  it  is  9  minutes'  ride  in  the  cars  out  to  Lakewood,  how 
many  minutes  does  it  take  a  car  to  go  four  times?  five 
times  ? 


PROCESSES   IN   WRITTEN   ARITHMETIC   CONTINUED.      425 

If  the  cook  fries  72  oysters,  thus  allowing  9  oysters  to 
each  person  at  the  table,  how  many  persons  are  expected 
at  table  ?  If  each  person  ate  only  8  oysters,  how  many 
would  be  left  for  the  cook  ? 

If  I  have  72  pounds  of  flour,  and  use  -^^  of  it  at  each 
baking,  for  how  many  bakings  will  it  be  sufficient  ?  How 
many  pounds  shall  I  use  at  each  baking  ? 

How  many  square  feet  in  a  square  that  is  three  feet  on  a 
side  ?  If  the  square  is  three  feet  on  a  side,  how  many 
yards  on  a  side  is  it  ?  Then  in  a  square  yard  how  many 
square  feet  ?     In  9  square  yards  how  many  square  feet  ? 

In  a  square  that  is  9  yards  on  a  side  how  many  square 
yards  ?  Which  do  you  think  is  the  larger  area,  9  square 
yards  or  a  square  9  yards  on  a  side  ? 

A  pole  7  feet  long  is  how  many  inches  long  ? 

A  man  6  feet  tall  measures  how  many  inches  in  height  ? 

If  8  benches,  each  a  foot  from  the  floor,  are  piled  top  of 
each  other,  how  much  higher  will  they  be  than  I,  who  am 
5  feet  and  6  inches?  If  I  can  reach  up  two  feet  above  my 
height,  how  near  can  I  come  to  reaching  the  top  bench  ? 

If  a  boy  earns  $8.00  per  month,  what  will  he  earn  in  a 
year  ?  If  he  spends  one-third  of  this  sum  for  clothes,  how 
much  will  he  have  lefk  ? 

In  one  gallon  how  many  gills  ? 

In  one  bushel  how  many  pints? 

In  one  rod  how  many  yards? 

In  one  rod  how  many  feet? 

In  one  rod  how  many  inches? 

In  one  week  how  many  hours  ? 

In  half  a  day  how  many  minutes  ? 

In  an  hour  how  many  seconds  ? 

If  12  dozen  pens  are  a  gross  of  pens,  how  many  pens  in  a 

3? 

In  16  pounds  how  many  ounces  ? 


426  FIRST  STEPS   IN   NUMBER. 

A  furlong  is  an  eiglitli  of  a  mile.  How  many  rods  are 
in  a  furlong  ? 

It  is  -|  of  a  mile  to  school.  How  many  eighths  less  than 
a  mile  is  it  ? 

If  you  have  |  of  a  dollar  and  spend  ^,  how  many  fourths 
of  a  dollar  have  you  left  ? 

I  ordered  a  pound  of  cheese,  but  the  grocer  cut  off  only 
f  of  a  pound.     How  much  less  than  a  pound  did  I  get  ? 

If  the  milliner  uses  f  of  a  yard  of  one  kind  of  velvet  in 
trimming  a  hat  and  f  of  a  yard  of  another  kind  of  velvet, 
how  much  more  of  one  kind  does  she  use  than  of  the  other? 

If  I  have  -5-  of  a  dollar  and  you  have  ^  of  a  dollar,  how 
many  more  fourths  have  I  than  you  ? 

If  I  buy  }  of  a  pound  of  sugar  and  i  of  a  pound  of  tea, 
how  much  more  sugar  than  tea  do  I  buy? 

Of  J  a  pound  of  meat,  -J-  of  a  pound  was  fat  and  gristle. 
How  many  sixths  of  a  pound  was  lean  ? 

I  had  i  of  a  yard  of  smilax,  but  -^^  of  a  yard  got  broken 
off.     How  many  tenths  of  a  yard  had  I  then  ? 

I  had  a  half-foot  ruler,  but  my  little  brother  whittled  off 
of  one  end  ^^  of  a  foot.  How  many  twelfths  of  a  foot  long 
was  my  ruler  then  ? 

I  had  |-  of  a  quire  of  paper,  but  h*ave  used  |-  of  a  quire 
of  the  paper.     How  many  eighths  of  a  quire  have  I  now  ? 

If  you  have  ^  of  a  ton  of  coal  in  a  bin,  and  use  ^^  of  a 
ton,  how  many  twelfths  of  a  ton  remain  in  the  bin? 

If  you  have  -J-  of  a  bunch  of  envelopes,  and  use  -|-  of  a 
bunch,  how  many  sixths  of  a  bunch  remain  ? 

A  basket  and  some  grapes  in  the  basket  together  weigh 
■|-  of  a  pound.  If  the  basket  weigh  -|-  of  a  pound,  how  many 
ninths  of  a  pound  do  the  grapes  weigh  ? 

A  boy,  in  carrying  a  measure  which  contained  -|-  of  a 
bushel  of  meal,  spilt  ^  of  a  bushel.  How  many  twelfths 
of  a  bushel  were  then  in  the  measure  ? 


PROCESSES   IN   WRITTEN   ARITHMETIC  CONTINUED.      427 

It  is  -J-  of  a  mile  across  the  green.  -^  of  Si  mile  is  shaded. 
What  part  of  a  mile  is  not  shaded  ? 

If  one  furlong  is  |-  of  a  mile,  how  many  eighths  of  a 
mile  are.  five  furlongs  ? 

If  it  takes  f  of  a  yard  of  lace  for  one  sleeve,  how  many 
sixths  will  it  take  for  2  sleeves  ?  for  3  ?  for  4  ?  for  6  ? 

If  it  is  "I  of  a  mile  to  town,  and  I  walk  the  distance  four 
times  a  day,  how  many  thirds  of  a  mile  do  I  walk  ?  how 
many  miles? 

If  a  man  is  28  years  old  and  his  son  is  J  as  old,  how  old 
is  the  son  ? 

If  you  have  collected  four  dozen  stamps,  of  which  one- 
fourth  are  foreign  stamps,  how  many  foreign  stamps  in 
your  collection  ? 

If  a  yard  of  cloth  costs  f  1.37,  what  will  7  yards  cost? 

If  there  were  but  30  days  in  each  month,  how  many  days 
would  there  be  in  a  year  ? 

If  I  have  25  quarters  of  a  dollar,  what  number  of  cents 
do  I  have  ? 

I  bought  19  yards  of  silk  at  $0.76  a  yard,  and  3  yards  of 
velvet  at  $1.50  a  yard.    What  was  the  amount  of  my  bill? 

What  will  95  street  lamps  cost  at  $  11.00  each? 

If  a  cannon-ball  weighs  12  pounds,  what  will  a  dozen 
cannon-balls  weigh  ? 

If  a  bale  of  hay  weighs  280  pounds,  what  will  65  bales 
weigh  ? 

If  your  pulse  beats  65  times  a  minute,  how  many  times 
will  it  beat  in  an  hour? 

If  from  the  sea  to  the  base  of  a  hill  there  is  a  rise  of  425 
feet,  and  the  hill  is  2  times  as  high  as  this  rise,  how  far 
above  the  sea  is  the  summit  of  the  hill  ? 

It  is  160  rods  across  a  pond,  and  three  times  as  far 
around  the  pond ;  how  many  rods  do  I  row  if  I  cross  the 
pond,  go  entirely  round  the  pond,  and  then  cross  again  to 
the  place  from  which  I  started  ? 


428  FIKST  STEPS   IN   NUMBER. 

How  many  sheets  of  paper  in  a  ream  of  paper  ? 

In  100  pints  how  many  quarts  ? 

In  80  gills  how  many  pints  ? 

In  160  quarts  how  many  gallons  ? 

In  240  quarts  how  many  pecks  ? 

In  99  feet  how  many  yards  ? 

In  a  mile  how  many  spaces,  each  8  rods  long,  can  you 
layoff? 

If  a  man  has  a  piece  of  ground  containing  180  square 
feet,  and  it  takes  9  square  feet  to  make  a  square  yard,  how 
many  square  yards  in  his  piece  of  ground  ? 

If  in  a  bed  of  plants  there  are  155  plants  set  out  in  rows 
with  5  plants  in  each  row,  how  many  rows  of  plants  in  the 
bed? 

If  a  cord  of  wood  is  worth  $  6,  and  10  cords  of  wood  are 
given  for  12  thousand  shingles,  how  much  are  the  shingles 
a  thousand  ? 

A  man  bought  an  equal  number  of  pigs  and  sheep  for 
$63.  Each  pig  cost  $3,  and  each  sheep  $4.  How  many 
of  each  did  he  buy  ? 

A  woman  bought  24  yards  of  gingham  at  $0.30  a  yard, 
and  23  yards  of  cotton  cloth  at  $0.10  a  yard.  How  much 
change  did  she  receive  out  of  a  ten-dollar  bill  ? 

A  man  can  do  a  piece  of  work  in  4  days  by  working 
12  hours  a  day.  How  many  days  will  be  required  if  he 
works  only  8  hours  a  day  ? 

A  man  can  do  a  piece  of  work  in  6  days  by  working  8 
hours  a  day.  How  many  hours  a  day  must  he  work  to 
finish  it  in  4  days  ? 

Two  men  are  96  miles  apart,  and  are  travelling  toward 
each  other,   one  at  the  rate  of  5  miles  an  hour,  and  the 
other  at  3  miles  an  hour.    In  how  many  hours  will  they 
meet? 
,    If  2  yards  of  silk  cost  $4,  what  will  5  yards  cost  ? 


CHAPTER  XXXyi. 

FRACTIONS. 


§  77.     Reduction  of  Fractions. 

Pirst  Step.  Reduce  improper  fractions  to  whole  or  mixed 
numbers.     Thus,  f-=l;  i  =  l;  |  =  1;  |^3;  |--lf. 

Second  Step.  Reduce  to  equivalent  fractions  of  higher 
terms.     Thus,  J  ^  f  ;  ^  =  i',  i  =  | ;  i  =-  f 

Third  Step.  Reduce  to  equivalent  fractions  of  lower 
terms.     Thus,  |  =  i;  |  =  i;  |  =  i;  1  =  ^. 

Fourth  Step.  Reduce  a  whole  or  mixed  number  to  an 
improper  fraction.     Thus,  2  =  f ;  2=-f;  2|-=|;  2|=:|. 

Fifth  Step.    Reduce  to  least  common  denominator. 

Exercise  for  Fourth  Step. 

If  I  get  a  two-dollar  bill  changed,  receiving  half-dollars 
for  it,  how  many  half-dollars  shall  I  receive  ? 

If  you  lend  me  2  dollars,  and  I  return  the  money  in 
quarters,  how  many  quarters  must  I  give  you  ? 

If  you  cut  2  pies  of  equal  size  into  eighths,  how  many 
eighths  of  a  pie  will  you  make  ? 

If  you  cut  two  saucer  pies  into  thirds,  how  many  thirds 
of  a  pie  will  you  make  ? 

If  you  cut  2  yards  of  cloth  into  strips,  each  I-  of  a  yard 
wide,  how  many  strips  will  you  have  ? 

If  a  man  puts  two  gallons  of  cider  into  bottles,  each  hold- 
ing 3-  of  a  gallon,  how  many  bottles  will  he  use? 


430  FIRST  STEPS   IN   NUMBER. 

If  we  burn  -^  of  a  ton  of  coal  a  day,  how  long  will  2  tons 
last  us  ? 

Express  this  number  (2)  in  halves;  in  fourths;  in 
eighths ;  in  thirds ;  in  sixths ;  in  sevenths ;  in  fifths  ;  in 
ninths ;  in  twelfths. 

Express  this  number  (4)  in  halves ;  in  thirds ;  in  fourths ; 
in  eighths. 

Express  any  number  you  please  in  halves.  Express  the 
same  number  in  other  fractions. 

If  it  is  2i  miles  to  West  Rock,  how  many  halves  of  a  mile 
is  it  to  West  Rock  ? 

If  I  buy  2 J  yards  of  ribbon,  how  many  thirds  of  a  yard 
do  I  buy  ? 

If  you  have  a  2-dollar  bill  and  a  quarter  of  a  dollar,  and 
I  have  the  same  amount  of  money  in  quarters,  how  many 
quarters  have  I  ? 

If  I  have  2^  barrels  of  kindling  wood,  how  many  fifths 
of  a  barrel  do  I  have  ? 

If  a  strip  of  carpeting  is  2^  yards  long,  how  many 
sixths  of  a  yard  in  the  strip  ? 

Express  2y  in  sevenths. 

Express  2-|-  in  eighths. 

Express  2^  in  ninths. 

Express  2^  in  twelfths. 

Express  the  numbers  I  name,  in  halves  :  4|-,  7|-,  10|-,  11-|-. 

Express  in  fourths:  3^,  3f,  5f,  6f,  9f,  11|. 

Express  in  thirds:  5^,  5|,  7-1,  7|,  12|,  llf,  9|. 

Express  in  eighths:  2f,  2|,  5f,  7|,  9|,  llf,  12|. 

Express  in  sixths :  2f ,  3f ,  4|-,  Gf. 

Express  in  fifths :  2|,  3|,  8f ,  9f . 

Express  in  sevenths :  2f ,  3-f-,  4-f-,  5f ,  6|-. 

Exercise  for  Fifth  Step. 

I  bought  I"  of  a  yard  of  one  kind  of  satin  and  ^  of  a 


FRACTIONS.  431 

yard  of  an  other  kind  of  satin.  Who  can  tell  me  in  sixths 
what  part  of  a  yard  of  each  kind  I  bought  ? 

If  I  pay  "I-  of  a  dollar  for  a  book  and  |-  of  a  dollar  for 
some  note  paper,  how  many  tenths  of  a  dollar  do  I  pay  for 
each  ? 

If  I  have  -J-  of  a  cord  of  hard  wood  and  -^  of  a  cord  of 
kindling  wood,  how  many  fourteenths  of  a  cord  of  each 
kind  do  I  have  ? 

If  you  are  in  one  school  -J-  of  the  year  and  in  another  -|-  of  a 
year,  how  many  eighteenths  of  a  year  are  you  in  each  school? 

Who  will  express  on  the  board  ^  and  ^  in  fractions 
having  their  denominators  alike  ? 

Who  will  express  ^  and  -^  in  fractions  having  their  de- 
nominators alike  ?     ^  and  ^  ?     -|-  and  -^  ? 

Who  will  express  \  and  \  in  fractions  having  their  de- 
nominators alike ?  ^  and  ^?  \  and  -^ ?  ^  and  ^?  ^,  ^, 
and  i  ?  II  and  i?  |,  I  and  ^?  l,  i  and  j\?  i  j, 
and^-V?  ii  audi?  iand|?  |,iandi?  i  i  and 
1^?     iiand^? 

When  you  change  fractions  to  other  fractions  whose 
denominators  are  alike,  we  say  that  you  reduce  the  fractions 
to  fractions  having  a  common  denominator.  When  you 
changed  ^  and  -J-  to  f  and  f,  you  reduced  ^  and  ^  to  equiv- 
alent fractions  having  a  common  denominator.  When  you 
changed  ^  and  ^  to  tenths,  what  do  we  say  you  did? 
When  you  changed  ^  and  \  to  twelfths,  what  did  you  do  ? 
When  I  ask  you  to  reduce  ^  and  ^  to  fractions  having  a 
common  denominator,  to  what  will  you  change  the  frac- 
tions ?  When  you  reduce  ^,  ^,  and  ^  to  fractions  having 
a  common  denominator,  to  what  will  you  change  the 
fractions  ? 

Reduce  to  fractions  having  a  common  denominator  ^,  -J-, 
and  J  ;  ^,  |-,  and  -J  ;  I  and  | ;  |  and  1 ;  |,  |,  and  -^ ; 
|.  i,  and  f 


432  FIRST  STEPS   IN   NUMBER. 


§  78.   Addition  of  Fractions. 

First  Step.  Add  fractions  whose  denominators  are  alike 
and   whose   sum   is   less   than  one.     Thus,  f  +  f ;  i  +  ^ ; 

l-Li-ili-i     22. 
414'     6'    5'    5'     6''6'6' 

Second  Step.  Add  fractions  whose  denominators  are 
unlike,  but  whose  least  common  denominator  is  found  in 
one  of  the  fractions  to  be  added.     Thus,  -J-  +  ^ ;    i  +  g- ; 

i  +  i;  i  +  i;  i  +  i;  i  +  i  +  i;  i  +  i+iV;  l  +  l- 

Third  Step.  Add  fractions  whose  denominators  are  un- 
like and  whose  least  common  denominator  is  not  found  in 
any  one  of  the  fractions  to  be  added.     Thus,  |-  +  | ;  i+i- 

Pourth  Step.    Add  mixed  numbers.     Thus,  3i-  +  5i. 

Exercise  for  Third  Step. 

It  takes  -|-  of  a  yard  of  lace  for  my  sleeves,  and  ^  of 
a  yard  for  my  collar.  I  want  you  to  find  what  part  of  a 
yard  it  takes  for  both  neck  and  sleeves.  "Who  can  tell  me 
the  least  common  denominator  of  |-  and  ^?  Then  give  me 
your  answer  in  sixths. 

A  man  earns  |-  of  a  dollar  an  hour,  and  his  son  earns  ^ 
of  a  dollar  an  hour.  What  part  of  a  dollar  do  they  earn 
together  ?  What  is  the  least  common  denominator  of  \ 
and  I"?     Then  find  your  answer  in  tenths. 

It  is  -J-  of  a  mile  to  the  post-ofiice  and  ^  of  a  mile  farther 
to  the  depot.  What  part  of  a  mile  is  the  distance  to  the 
depot  ?  To  what  will  you  reduce  the  fractions  ?  What  is 
your  number  of  twelfths  ? 

Find  the  sum  of  |-,  \,  and  ^.  What  is  the  least  common 
denominator  ? 

Find  the  sum  of  -J,  -|,  and  -J-. 

Find  the  sum  of  ^,  ^,  and  ^. 

Find  the  sum  of  i,  -l-,  and  -J-. 


Find  the  sum  of  ^  and  f. 


FRACTIONS.  433 

Find  the  sum  of  \  and  f ;  \  and  f. 
Find  the  sum  of  |,  ^,  and  ^ ;  f  and  f. 

Exercise  for  Fourth  Step. 

In  one  piece  of  trimming  there  are  4|-  yards,  and  in 
another  piece  of  the  same  trimming  there  are  11-|-  yards. 
I  want  you  to  find  how  many  yards  there  are  in  both 
pieces.  You  may  add  your  fractions  first  in  all  such 
numbers.  What  is  the  sum  of  the  fractions  ?  What  is  the 
sum  of  the  other  numbers?     What  is  the  entire  sum? 

Try  if  you  can  add  19^  and  17^  ;  15|  and  75^ ;  12-i-  and 
9^  ;  8|  and  7|;  9^  and  6| ;  5^  and  9f .' 

§  79.   Subtraction  of  Fractions. 
Pirst  Step.     Subtract  fractions  having  like  denominators. 

TVina     3  1.6  3.4  3.5  2 

inus,  -J  — :j,    8"  — -g",    T       T'    ¥        d- 

Second  Step.  Subtract  fractions  whose  denominators  are 
unlike,  but  whose  least  common  denominator  is  found  in 
one  of  the  given  fractions.     Thus,  -J— i;  -f—i;  i~h 

Third  Step.  Subtract  fractions  whose  denominators  are 
unlike,  but  whose  least  common  denominator  is  not  found 
in  any  one  of  the  given  fractions.     Thus,  I-— f  ;  •j-'^f  • 

PoTirth  Step.    Subtract  one  mixed  number  from  another. 

Exercise  for  Third  Step. 

From  I"  of  a  barrel  of  vinegar  I  have  drawn  off  -|-  of  a 
barrel  of  vinegar.   What  part  of  a  barrel  of  vinegar  remains  ? 

What  must  you  do  before  you  can  find  the  difference 
between  ^  and  ^?  What  is  the  least  common  denominator  ? 
What  do  you  find  your  answer  to  be  ? 

A  book  which  I  bought  cost  ^  of  a  dollar.  I  paid  for  it 
with  -J-  of  a  dollar.  What  part  of  a  dollar  ought  I  to 
receive  in  change  ? 

Find  the  difference  between  -f  and  ^, 


434  FIRST  STEPS   IN   NUMBER. 


Find  the  diiFerence  between  f  and  ^, 


Find  the  diiFerence  between  |-  and 

Find  the  difference  between  -f-  and  ^ ;  f  and  ^. 

Find  the  difference  between  f  and  f ;  -f  and  |. 

Exercise  for  Fourth  Step. 

There  were  2^  yards  cut  from  a  pole  which  was  a  rod  in 
length.  I  wish  to  know  how  many  yards  in  length  the  pole 
was  then.  If  only  ^  of  a  yard  had  been  taken  from  5|- 
yards,  how  long  would  the  pole  be  ?  If  2  yards  more  were 
cut  off,  what  then  remained  ?  How  long  then  was  the  pole 
that  lacked  2^  yards  of  being  a  rod  long  ? 

If  a  room  is  lOf  feet  high,  and  the  bordering  and  dado 
take  up  4-|-  feet,  what  is  the  distance  between  the  bordering 
and  the  dado  ?  Find  first  what  would  be  the  distance  if 
only  ^  foot  were  taken  up.  Find  next  what  was  the  dis- 
tance when  4  more  feet  were  taken. 

Find  the  difference  between  8|-  and  3| ;  72f  and  19^ ; 
70J  and  15^ ;  63f  and  29|- ;  85f  and  27f  ;  62f  and  37f 

§  80.   Multiplication  of  Fractions. 

First  Step.  Multiply  a  fraction  by  an  integer.  Thus,  2 
times  "I ;  3  times  -| ;   3  times  j-. 

Second  Step.  Find  fractional  parts  of  numbers.  Thus, 
^  of  16  ;  I  of  12  ;  f  of  20  ;  f  of  24  ;  I  of  30  ;  4-  of  28. 

Third  Step.  Multiply  one  fraction  by  another  when  the 
operation  can  be  performed  by  dividing  the  numerator  of 
the  multiplicand  by  the  denominator  of  the  multiplier. 
Thus,  i  of  4;  ioff;  \oi^;  ^off;  iofif. 

I  had  -|  of  a  dollar,  and  spent  ^  of  what  I  had.  Let  us 
find  how  many  eighths  of  a  dollar  I  spent.  If  the  eighths 
of  a  dollar  had  been  whole  dollars,  and  I  spent  ^  of  it,  how 
many  dollars  should  I  have  spent  ?  If  ^  of  6  dollars  is  3 
dollars,  then  ^  of  f  is  how  many  eighths  ? 


FRACTIONS.  435 

If  I  cut  -|  of  a  yard  of  ribbon  into  4  equal  parts,  how 
many  ninths  of  a  yard  were  in  each  part  ?  If  I  had  cut  8 
yards  of  ribbon  into  4  equal  parts,  how  many  yards  would 
there  be  in  each  part  ?  If  ^  of  8  yds.  ==  2  yds.,  then  -J  of  | 
will  equal  how  many  ninths  ? 

^  of  ^  equals  how  many  sevenths  ? 

■1-  of  -j^  equals  how  many  elevenths? 

■g-  of  -^  equals  how  many  thirteenths  ? 

1  of  3^  equals  how  many  elevenths  ? 

^  of  -fl  equals  how  many  eighteenths  ? 

-|-  of  |-^  equals  how  many  twenty-firsts  ? 

-1-  of  -^  equals  how  many  twentieths  ? 

•^  of  f^  equals  how  many  twenty- fourths? 

§  81.   Division  of  Fractions. 

Pirst  Step.  Divide  fractions  when  the  denominators  are 
alike,  and  the  numerator  of  the  dividend  is  exactly  divis- 
ible by  the  numerator  of  the  divisor.  Thus,  f  ^  f ;  t\  "^  t\- 

Second  Step.  Divide  fractions  when  the  denominators 
are  alike,  but  the  numerator  of  the  dividend  is  not  exactly 
divisible  by  the  numerator  of  the  divisor.     Thus,  i  -h-  f . 

Exercise  for  First  Step. 

I  have  here  an  orange  cut  into  12  equal  parts.  To  how 
many  children  can  you  give  ^  of  an  orange,  if  you  give 
■j^  to  each  child  ?     In  -j^  then  how  many  times  ^  ? 

John,  you  may  take  -^  of  the  orange,  and  give  ^  to  each 
child  until  you  have  none  left.  To  how  many  children  did 
you  give  ^,  giving  -^  to  each  child  ?  How  many  times  is 
-j^  found  in  ^  ? 

Annie,  you  may  take  -]-|,  and  find  how  many  times  -^  is 
found  in  ■^.     Find  how  many  times  -^  is  found  in  ^. 

How  many  times  is  ^  found  in  ^?  y2-  in  ^?  y^"  ^^  A^ 


436  FIRST  STEPS   IN   NUMBER. 

If  I  have  f  of  a  dollar,  and  buy  crackers  at  -|  of  a  dollar 
a  pound,  how  many  pounds  do  I  buy?  If  the  crackers 
were  f  of  a  dollar  a  pound,  how  many  pounds  could  I  buy? 

If  I  have  y^^  of  a  lb.  of  coffee,  and  I  use  y^-  each  day,  how 
many  days  will  the  coffee  last  ?  If  I  use  only  ^^  of  a  lb.  a 
day,  how  many  days  will  the  coffee  last  ?  If  I  use  y\  a 
day,  how  many  days  will  -^  last  ? 

If  it  takes  me  -^-^  of  an  hour  to  write  a  line,  how  many 
times  can  I  write  the  line  in  |^  of  an  hour  ?  If  it  takes 
me  -g^o"  of  an  hour,  how  many  times  can  I  write  the  line  ? 
If  it  takes  me  -g^  of  an  hour  to  write  a  long  line,  how  many 
times  can  I  write  it  in  |4.  of  an  hour  ?  If  James  can  copy 
his  spelling  in  -^-^  of  an  hour,  how  many  times  can  he  copy 
his  spelling  in  |^  of  an  hour  ?  If  it  takes  Nellie  q\  of  an 
hour,  how  many  times  can  she  copy  her  words  in  |-|-  of  an 
hour  ?  If  it  takes  a  car  -|-|  of  an  hour  to  make  a  trip,  liow 
many  trips  can  the  car  make  in  -||-  of  an  hour  ? 

Divide  ^  by  ,^;  I  by  I;  if  by  y^ ;  i|  by  ^. 

Exercise  for  Second  Step. 

It  takes  f  of  a  yard  of  cloth  for  an  apron.  Who  will  tell 
me  how  many  aprons  I  can  make  from  -|  of  a  yard  ?  (3.) 
What  part  of  a  yard  will  remain  after  I  take  enough  for  3 
aprons?  What  part  of  enough  for  an  apron  is  -|-  of  a  yard? 
How  many  aprons  and  what  part  of  an  apron  can  I  make 
from  -|  of  a  yard,  if  it  takes  -|  of  a  yard  for  each  apron  ? 

My  bottle  of  ink  is  -^  full.  If  I  use  -j^  of  a  bottle  each 
month,  how  many  months  will  the  ink  last  me?  (4 
months.)  At  the  end  of  four  months,  what  part  of  a  bottle 
of  ink  will  remain?  (iV-)  What  part  of  a  month  will  -^ 
last  me,  if  I  use  ^  each  month  ?  How  many  months  and 
what  part  of  a  month  will  -^^  of  a  bottle  of  ink  last,  if  I 
use  -j^  each  month  ? 

How  much  cake  can  I  make  from  -ff  of  a  dozen  eggs,  if 
y\  of  a  dozen  are  required  for  each  pound  of  cake  ? 


FRACTIONS.  437 

If  a  boy  earns  -^  of  a  dollar  a  day,  in  what  time  will  he 
earn  f  f  of  a  dollar  ? 

If  a  ship  sails  -^  of  a  mile  in  a  minute,  in  what  time  will 

it  sail  f  I"  of  a  mile  ? 

If  a  pound  of  coffee  costs  -^-^  of  a  dollar,  what  amount  of 

coffee  can  I  buy  for  a  dollar? 

If  crackers  are  -^  of  a  dollar  a  pound,  what  amount  of 
crackers  can  be  bought  for  a  dollar  ? 

Divide  f  by  | ;  by  f ;  by  | ;  by  f . 

Divide  ^  by  ^;  by  T^;  by  3^  ;  by  ^. 

Divide  if  by  tV;  by  ^;  by  -3^;  by  ^. 

Exercise  for  Review. 

A  slate  pencil  and  a  lead  pencil  together  cost  4  cents. 
If  the  lead  pencil  cost  three  times  as  much  as  the  slate 
pencil,  what  did  each  pencil  cost  ? 

A  slate  and  a  pencil  together  cost  9  cents.  What  did 
each  cost,  if  the  slate  cost  twice  as  much  as  the  pencil  ? 

A  piece  of  baize  for  a  desk  cover  and  the  braid  to  bind 
it,  together  cost  15  cents.  If  the  braid  cost  only  half  as 
much  as  the  baize,  what  did  each  cost  ? 

I  bought  some  pens  and  a  penholder  for  12  cents.  The 
penholder  cost  twice  as  much  as  the  pens.  "What  did  the 
pens  cost? 

I  bought  some  stamps  and  an  envelope  for  10  cents. 
The  stamps  cost  four  times  as  much  as  the  envelope.  How 
much  did  each  cost  ? 

An  apple  and  a  peach  together  cost  6  cents.  The  peach 
cost  twice  as  much  as  the  apple.     What  did  the  apple  cost? 

Suppose  you  and  I  are  20  rods  apart,  and  you  gain  upon 
me  2  rods  every  minute.  How  long  before  you  will  over- 
take me  ?  If  I  can  walk  20  rods  in  a  minute,  how  far  shall 
I  walk  while  you  are  catching  up  to  me  ?  How  far  will  you 
walk  ?     How  many  more  rods  must  I  walk  to  go  a  mile  ? 


438  FIRST  STEPS   IN  NUMBER. 

If  a  bicycle  goes  9  miles  .while  I  am  walking  3  miles, 
how  many  times  as  fast  as  I  does  the  bicycle  go  ?  While 
I  am  walking  2  miles,  how  far  will  the  bicycle  go?  If  the 
bicycle  and  I  start  together,  and  I  go  a  mile  and  return, 
how  many  miles  can  the  bicycle  go  and  return  in  the  same 
time? 

If  you  are  9  years  old  and  I  am  21  years  old,  how  old 
will  each  of  us  be  when  I  am  just  twice  as  old  as  you  ? 

If  it  costs  25  cents  to  send  a  telegram  consisting  of  10 
words,  and  2  cents  for  each  additional  word,  what  will  it 
cost  to  send  a  message  of  15  words  ? 

If  it  costs  $  5.00  for  a  table  6  feet  long,  and  50  cents  for 
every  additional  foot,  how  much  must  I  pay  for  a  table  10  J 
feet  long  ? 

If  it  takes  2  hours  to  roast  a  turkey  weighing  10  pounds, 
and  15  minutes  more  for  every  additional  pound,  how  long 
will  it  take  to  roast  a  turkey  weighing  14  pounds  ? 

How  many  tiles  4  inches  square  will  it  take  to  cover  a 
space  16  inches  square  ? 

A  meter  is  39|  inches.  What  is  the  difference  in  length 
between  a  yard  and  a  meter?  between  2  yards  and  2 
meters  ? 

If  you  have  I-  of  a  dollar,  and  I  have  J  of  a  dollar,  how 
many  pounds  of  candy  can  we  buy  at  ^  of  a  dollar  a  pound  ? 

If  one  man  owns  |-  of  a  building  lot  and  another  man 
owns  f  of  the  lot,  how  much  of  the  building  lot  do  both 
men  own  ? 

If  I  ride  |-  of  a  mile  and  walk  -I  of  a  mile,  what  part  of 
a  mile  do  I  go  ? 

If  you  study  one  lesson  -^  of  an  hour  and  another  lesson 
^  of  an  hour,  what  part  of  an  hour  do  you  spend  studying? 

If  there  is  I-  of  a  dozen  buttons  on  one  card,  :|  of  a  dozen 
on  another  card,  and  ^  of  a  dozen  on  yet  another  card, 
what  part  of  a  dozen  is  on  all  the  cards  together  ? 


FRACTIONS.  439 

If  I  have  ^  of  a  card  of  matches  and  |  of  a  card,  what 
part  of  a  card  have  I  all  together  ? 

If  you  have  |-  of  a  dollar  and  I  have  3-  of  a  dollar,  how 
much  money  have  we  together  ? 

What  is  the  sum  of  I  and  I?  ^andf?  fand-i-?  | 
andf?     I,  i  and  I?     fandf?     |and-|? 

If  for  dinner  we  eat  ^  and  ^  of  a  melon,  what  part  of 
the  melon  is  left  ? 

I  bought  f  of  a  peck  of  sweet  potatoes,  and  we  have 
eaten  ^  of  a  peck.  What  part  of  a  peck  remains  ?  How 
many  more  eighths  of  a  peck  must  I  have  to  make  a 
whole  peck  ? 

If  my  bottle  of  ink  is  half  full,  and  I  use  -f  of  a  bottle  of 
ink,  what  part  of  a  full  bottle  will  remain  ? 

If  from  f  of  a  cask  of  vinegar  f  of  the  cask  is  drawn  off, 
what  part  of  a  full  cask  remains  ?  If  the  cask  holds  48 
gallons,  how  many  gallons  remain  in  the  cask  ? 

If  |-  of  a  bushel  of  corn  is  taken  from  a  basket  holding  f 
of  a  bushel,  what  part  of  a  bushel  will  remain? 

What  is  the  difference  between  f  and  f?  ^  and  f  ?  f 
and  ■§-  ?     "I  and  f  ? 

If  you  earn  -I  of  a  dollar  a  week,  how  much  will  you 
earn  in  6  weeks?  in  9  weeks?  in  11  weeks? 

How  much  will  6  books  cost  at  f  of  a  dollar  a  book  ?  at 
I"  of  a  dollar  a  book  ?  at  -J-  of  a  dollar  a  book  ? 

In  one  bunch  of  bananas  there  were  20  bananas.  When 
f  of  the  bunch  have  been  sold,  how  many  bananas  have 
been  sold  ? 

If  a  yard  of  cloth  costs  48  cents,  what  must  I  pay  for  f 
of  a  yard  ? 

When  apples  are  60  cents  a  bushel,  what  must  you  pay 
for  -f^  of  a  bushel  ? 

In  "I  of  a  yard  how  many  inches  ? 

In  |-  of  an  hour  how  many  minutes? 


440  FIRST  STEPS   IN   NUMBER. 

In  |-  of  a  bushel  how  many  quarts? 

A  man  cut  f  of  a  cord  of  wood  in  a  day,  and  his  son  cut 
•J  as  much.     How  many  ninths  did  the  son  cut? 

I  have  3^  of  a  dozen  eggs  in  one  basket  and  ^  as  many 
eggs  in  another  basket.  What  part  of  a  dozen  have  I  in 
the  second  basket  ? 

In  our  back  yard  there  are  f  of  an  acre  of  land,  and  in 
the  front  yard  there  is  only  -J  as  much  land.  How  many 
sevenths  of  an  acre  in  the  smaller  yard  ? 

I  have  a  piece  of  ribbon  f  of  a  yard  long.  If  I  cut  off  -^ 
of  the  ribbon,  what  part  of  a  yard  shall  I  cut  off? 

I  had  in  my  purse  ^^  of  a  dollar,  but  I  spent  \  of  my 
money.     What  part  of  a  dollar  did  I  spend  ? 

WhatisiofnUofMUofA? 

Whatisiof||?iofH?iof||? 

When  apples  are  f  of  a  dollar  a  peck,  how  many  pecks 
can  I  buy  for  |-  of  a  dollar  ? 

If  we  use  I"  of  a  pound  of  butter  at  a  meal,  for  how  many 
meals  will  f  of  a  pound  be  sufficient  ? 

If  we  use  -^  of  a  pound  of  coffee  in  a  day,  in  how 
many  days  shall  we  use  -^-^  of  a  pound  ? 

If  I  eat  -j^  of  a  pound  of  meat  each  meal,  how  many 
meals  will  ^  of  a  pound  last  me  ? 

If  ice  forms  at  the  rate  of  -^-^  of  an  inch  an  hour,  how 
long  will  it  take  for  the  ice  to  be  an  inch  thick  ?  6  inches 
thick  ?  9  inches  thick  ?  a  foot  thick  ? 

If  a  vine  grows  -f^  of  an  inch  a  day,  how  many  days  will 
it  take  the  vine  to  grow  9  inches  ? 

A  drover  paid  $200  for  lambs  at  $5.00  apiece.  How 
many  lambs  did  he  buy  ? 

A  man  paid  $2.10  for  eggs  at  $0.30  a  dozen.  How 
many  dozen  of  eggs  did  he  buy  ? 

I  bought  3  bookcases,  one  for  $35.00,  one  for  $12.00, 
and  one  for  $8.00,  and  paid  $5.00  for  having  them  var- 


FRACTIONS.  441 

nished.  At  the  end  of  5  years  I  sold  them  for  $30.00.  If 
they  were  worth  $  6.00  a  year  to  me  while  I  had  them,  did 
I  gain  or  lose  ? 

I  bought  40  yards  of  carpeting  for  $0.75  a  yard,  and 
after  using  the  carpet  5  years  I  sold  it  for  $  15.00.  If  the 
carpet  was  worth  $3.00  a  year  to  me,  did  I  gain  or  lose? 

A  man  bought  a  second-hand  chamber  set  for  $  25.00, 
and  paid  $3.00  to  put  it  in  good  order,  then  sold  it  for 
$40.00.     How  much  did  he  make  ? 

If  it  takes  $84.00  to  furnish  a  school-room  with  seats  at 
$2.00  each,  how  many  are  put  into  the  room? 

If  the  uniforms  for  a  company  of  boys  cost  $  189.00,  at 
$3.00  each,  how  many  boys  are  in  the  company? 

If  a  merchant  sells  $  168.00  worth  of  boots  in  a  week, 
at  $4.00  a  pair,  how  many  pairs  does  he  sell  ?  What  does 
he  gain  at  25  cents  a  pair  ? 

A  man  sold  -|  of  a  piece  of  cotton  cloth  which  contained 
45  yards.  How  many  yards  did  he  sell?  How  many 
yards  were  left  ? 

A  horse  cost  $200,  and  a  sleigh  f  as  much.  What  did 
the  sleigh  cost  ? 

A  man  owned  f |  of  a  ship,  and  sold  ^  of  his  share.  How 
many  sixty-fourths  had  he  left  ? 

John  had  |  of  a  dollar,  and  George  and  Charles  had  each 
^  of  a  dollar.  How  much  more  had  George  and  Charles 
together  than  John  ? 

How  many  dollars  will  3  barrels  of  flour  cost  at  $  6|  a 
barrel  ? 

If  2  yards  of  cloth  cost  $8|-,  what  is  the  price  per  yard? 

How  many  pints  in  12|-  gallons  ?  How  many  gallons  in 
168  pints  ? 

How  many  pecks  in  248  quarts  ?     How  many  bushels  ? 

If  a  locomotive  can  go  8  miles  in  ^  of  an  hour,  how  many 
miles  can  it  go  in  one  hour  and  a  half? 


CHAPTEE  XXXVII. 

FACTORS. 


§  82.   A  Factor  of  a  Number. 

Name  a  number  that  will  divide  six  without  a  remainder. 
(2.) 

Two  is  2^  factor  of  six. 

Name  another  number  that  will  divide  six  without  a 
remainder.     (3.) 

Three  is  a  factor  of  six. 

Name  another  factor  of  six.     (1.) 

Name  another  factor  of  six.     (6.) 

Name  a  factor  of  twelve.     (3.) 

Name  another  factor  of  twelve.     (4.) 

Name  another  factor  of  twelve.     (6.) 

Name  another  factor  of  twelve.     (2.) 

Name  the  two  remaining  factors  of  twelve.     (1  and  12.) 

Name  the  factors  of  fifteen ;  of  eight ;  of  sixteen ;  of 
twenty;  of  twenty-four;  of  thirty-six;  of  forty-eight;  of 
seventy-two. 

"What  have  you  been  naming  of  numbers  ? 

What  is  true  of  a  factor  of  a  number  ? 

§  83.   Prime  and  Composite  Numbers. 

What  are  the  factors  of  seven  ?  three  ?  eleven  ?  fiNQ  ? 
thirteen?  seventeen?  twenty-three?  twenty-nine?  thirty- 
one?  forty-one? 


FACTORS.  443 

Name  another  number  of  which  the  factors  are  simply 
one  and  the  number  itself;  another  ;  another. 

Beginning  with  one,  write  in  order  a  dozen  numbers 
whose  factors  are  simply  one  and  the  number  itself. 

Describe  these  numbers  with  reference  to  their  factors. 

All  such  numbers  are  prime  numbers. 

Describe  a  prime  number.  Name  a  number  that  has 
other  factors  as  well  as  one  and  itself.  Who  thinks  of 
three  such  numbers? 

Write  a  score  of  such  numbers. 

Describe  these  numbers  with  reference  to  their  factors. 

All  such  numbers  are  composite  numbers. 

Describe  a  composite  number.  I  will  name  the  num- 
bers from  one  to  thirty,  and  you  may  describe  each  by 
saying  prime  or  composite  as  I  name. 

Are  most  numbers  prime  or  composite  ? 

§  84.   Prime  Factors  of  a  Number. 

Name  a  prime  number  that  is  a  factor  of  twelve.     (2.) 

Two  is  a  prime  factor  of  twelve. 

Name  another  prime  number  that  is  a  factor  of  twelve. 

Three  is  a  prime  factor  of  twelve.  Name  a  prime  factor 
of  sixteen ;  of  eighteen. 

Name  two  prime  factors  of  twenty-one ;  of  twenty-four ; 
of  twenty-eight ;  of  thirty-six  ;  of  thirty-five. 

What  kind  of  factors  have  you  been  naming  ?    . 

What  do  you  mean  by  a  prime  factor  of  a  number  ? 

Write  the  prime  numbers  whose  product  is  six ;  whose 
product  is  eight ;  whose  product  is  twelve  ;  whose  product 
is  sixteen ;  whose  product  is  eighteen ;  whose  product  is 
twenty  ;  whose  product  is  twenty-four. 

You  have  expressed  the  prime  factors  of  these  numbers. 


444  FIRST  STEPS   IN   NUMBER. 

Express  the  prime  factors  of  thirty;  of  thirty-two;  of 
thirty-six  ;  of  twenty-eight ;  of  twenty-seven. 
Complete  this  work : 

The  prime  factors  of  40  = 

The  prime  factors  of  42  = 

The  prime  factors  of  45  = 

The  prime  factors  of  44  = 

The  prime  factors  of  48  = 

The  prime  factors  of  49  = 

The  prime  factors  of  50  = 

The  prime  factors  of  54  = 

The  prime  factors  of  56  = 

The  prime  factors  of  60  = 

The  prime  factors  .of  63  = 

The  prime  factors  of  64  ~ 

The  prime  factors  of  66  = 

The  prime  factors  of  70  = 

The  prime  factors  of  72  = 

Find  the  product  of  the  factors  of  each  number,  and  see 
if  the  product  is  the  number  itself. 

What  are  the  prime  factors  of  any  number  ? 

§  85.   A  Common  Factor  of  Two  or  More  Numbers. 

Name  a  factor  of  four  that  is  also  a  factor  of  six.     (2.) 

Two  is  a  co7nmon  factor  of  four  and  six. 

Name  a  factor  of  four  that  is  a  factor  of  six,  eight,  and 
ten.     (2.) 

Two  is  a  common  factor  of  four,  six,  eight,  and  ten. 

Name  a  factor  of  six  that  is  a  factor  of  nine  and  of 
twelve.     (3.) 

Three  is  a  common  factor  of  six,  nine,  and  twelve. 

Name  a  common  factor  of  eight  and  twelve. 

Name  a  common  factor  of  six,  nine,  and  eighteen. 


FACTORS.  445 

Name  a  common  factor  of  seven,  fourteen,  and  twenty- 
one. 

Name  a  common  factor  of  ten,  fifteen,  and  twenty-five. 

Name  a  common  factor  of  nine,  twelve,  fifteen,  and 
twenty-four. 

What  is  true  of  a  common  factor  of  two  or  more  num- 
bers ? 

Name  all  tlie  factors  common  to  six  and  twelve. 

Which  of  these  common  factors  is  the  greatest  number  ? 

Six  is  the  greatest  common  factor  of  six  and  twelve. 

Name  all  the  factors  common  to  twelve  and  twenty-four. 

Which  of  these  common  factors  is  the  greatest  number? 

Twelve  is  the  greatest  common  factor  of  twelve  and 
twenty-four. 

Name  all  the  factors  common  to  eight,  twelve,  and 
twenty. 

Which  of  these  common  factors  is  the  greatest  number  ? 

What  is  four,  then,  of  eight,  twelve,  and  twenty  ? 

Name  the  greatest  common  factor  of  six,  twelve,  and 
eighteen ;  of  ten,  twenty,  and  thirty ;  of  eighteen  and 
thirty-six ;  of  fourteen  and  twenty-eight ;  of  sixteen  and 
twenty-four ;  of  twenty-four,  thirty,  and  thirty-six. 

What  is  the  greatest  common  factor  of  two  or  more 
numbers  ? 

§  86.   A  Multiple  of  a  Number. 

Name  a  number  of  which  two  is  a  factor.     (4.) 
Four  is  a  multiple  of  two. 

Name  another  number  of  which  two  is  a  factor.     (8.) 
Eight  is  a  multiple  of  two. 

Name  another  multiple  of  two  ;  another ;  another. 
Beginning  with  four,  write  the  multiples  of  two  as  far  as 
thirty. 


446  FIRST  STEPS   IN   NUMBER. 

Write  the  multiples  of  three  as  far  as  thirty. 
Write  the  multiples  of  four  as  far  as  forty. 
Write  three  multiples  of  five  ;  of  six  ;  of  seven  ;  of  eight ; 
of  nine  ;  of  ten. 

What  have  you  been  writing  ? 

What  do  you  mean  by  a  multiple  of  a  number  ? 

§  87.   A  Common  Multiple  of  Given  Numbers. 

Name  a  multiple  of  two  that  is  also  a  multiple  of  four. 
(8.) 

Eight  is  a  conmion  multiple  of  two  and  four. 

Name  another  common  multiple  of  two  and  four ; 
another ;  another. 

Name  a  common  multiple  of  two,  three,  and  four ;  of 
two,  four,  and  five ;  of  two,  four,  and  six ;  of  three  and 
five  ;  of  three  and  seven ;  of  six  and  nine ;  of  two,  three, 
four,  six,  eight,  and  twelve  ;  of  two,  three,  four,  six,  nine, 
twelve,  and  eighteen. 

What  do  you  mean  by  a  common  multiple  of  two  num- 
bers? 

Name  the  smallest  number  that  is  a  common  multiple  of 
two  and  three.     (6.) 

Six  is  the  least  common  multiple  of  two  and  three. 

Name  the  least  common  multiple  of  three  and  four ;  of 
two  and  five  ;  of  two  and  seven  ;  of  three  and  five  ;  of  two 
and  four  ;  of  three  and  six  ;  of  four  and  eight ;  of  four  and 
six ;  of  six  and  twelve  ;  of  four  and  seven. 

Name  the  least  common  multiple  of  two,  four,  and  eight ; 
of  three,  six,  and  twelve;  of  three,  four,  and  six;  of  two, 
four,  and  five ;  of  two,  five,  and  ten  ;  of  three,  five,  and 
ten  ;  of  four,  five,  and  ten  ;  of  two,  six,  and  ten ;  of  three, 
six,  and  ten. 


FACTORS.  447 


Exercise  for  Review. 


Express  the  factors  of  12  ;  of  18  ;  of  24 ;  of  36. 

Point  to  the  row  of  numbers  which  have  12  for  a 
multiple. 

Point  to  the  row  of  numbers  which  have  24  for  a 
multiple. 

Point  to  the  row  of  numbers  which  have  36  for  a 
multiple. 

Point  to  the  row  of  numbers  which  have  18  for  a 
multiple. 

Draw  a  line  through  each  number  that  is  not  found  in 
all  the  rows. 

What  word  will  describe  the  factors  that  remain  with 
reference  to  12,  18,  24  and  36? 

What  word  will  describe  6  as  a  common  factor  of  these 
numbers  ? 

Try  in  the  same  way  to  find  the  greatest  common  factor 
of  14,  28,  and  42. 

Find  the  greatest  common  factor  of  16,  24,  40,  and  48. 

Find  the  greatest  common  factor  of  20,  40,  60,  and  80. 

Find  the  greatest  common  factor  of  25,  50,  and  75. 

I  have  cloth  out  of  which  I  wish  to  cut  squares  for  a 
patchwork  quilt.  The  cloth  is  of  three  widths  :  12  inches, 
18  inches,  and  24  inches.  What  are  the  largest  squares  I 
can  get  without  any  waste  of  cloth  ? 

A  gardener  has  a  rectangular  flower-bed  which  is  6  feet 
on  each  of  two  sides,  8  feet  on  each  of  the  other  two  sides, 
and  10  feet  from  corner  to  corner.  If  he  borders  this 
flower-bed  with  plants  at  equal  distances  apart,  and  sets 
them  across  the  diagonals  at  the  same  distance  apart,  what 
is  the  greatest  distance  at  which  they  can  be  placed  from 
each  other? 

If  the  lengths  of  the  sides  and  diagonal  were  4,  3,  and  5 


448  FIRST  STEPS   IN   NUMBER. 

respectively,  what  would  be  tlie  greatest  distance  at  which 
plants  could  be  placed  to  be  the  same  distance  apart  ? 

If  the  lengths  were  12,  16,  and  20,  what  would  be  the 
greatest  distance  ? 

If  the  lengths  were  24,  32,  and  40,  what  would  be  the 
greatest  distance  ? 

I  have  some  paper  which  is  9  inches  wide,  some  which  is 
12  inches  wide,  and  some  which  is  15  inches  wide,  which  I 
wish  to  cut  into  strips  of  equal  width.  What  can  be  the 
greatest  width  of  the  strips  so  as  to  have  no  waste  of  the 
paper  ? 

Write  the  numbers  in  order  from  1  to  30. 

Draw  a  line  through  each  odd  number. 

Place  a  dot  over  each  prime  number. 

Is  every  odd  number  a  prime  number  ? 

What  even  number  is  a  prime  number  ? 

What  word  will  describe  all  numbers  not  prime? 

Are  all  composite  numbers  even  numbers  ? 

Are  all  even  numbers  composite  numbers? 

Are  there  more  composite  numbers  than  even  numbers? 

Name  the  prime  factors  of  6,  8,  9,  12,  18,  20,  24. 

Divide  48  by  one  of  its  prime  factors.  Divide  the  answer 
by  a  prime  factor.  Go  on  dividing  by  prime  factors  until 
the  answer  is  a  prime  number.  Find  the  product  of  the 
last  answer  and  the  several  divisors.    What  is  the  answer  ? 

What  then-  are  the  prime  factors  of  48  ? 

In  the  same  way  find  the  prime  factors  of : 

72       148       196       289 

144       200       225       324 

96       169       256       400 

Write  in  a  row  the  multiples  of  2  as  far  as  30. 

Write  the  multiples  of  3  as  far  as  30. 

Write  the  multiples  of  4  as  far  as  28. 

Draw  a  line  through  every  multiple  not  found  in  all  the 
rows. 


FACTORS.  449 

"What  word  will  describe  tlie  remaining  multiples  with 
reference  to  2,  3,  and  4  ? 

What  word  will  describe  12  as  a  common  multiple  of  2, 
3,  and  4  ? 

Write  the  multiples  of  6,  9,  and  4  until  you  find  the 
least  common  multiple  of  the  numbers. 

Find  the  least  common  multiple  of  2,  3,  4,  and  8. 

Find  the  least  common  multiple  of  3,  5,  and  2. 

Find  the  least  common  multiple  of  4,  5,  and  8. 

I  have  here  several  disks  of  paper.  You  will  see  that 
one  is  divided  into  halves,  another  into  thirds,  another  into 
fourths,  and  so  on,  each  being  divided  into  a  certain  num- 
ber of  equal  parts. 

I  wish  you  to  show  me  -J-  and  \  of  the  same  disk.  Which 
digk  will  you  choose  ?     (The  one  divided  into  fourths.) 

Which  disk  will  you  choose  to  show  me  ^  and  -|-  of  the 
same  one  ?     (The  one  divided  into  sixths.) 

Which  disk  will  you  choose  to  show  me  ^,  \,  and  -J-  ? 

Which  disk  to  show  me  |-  and  -|-? 

Which  disk  to  show  me  ^  and  -J-  ? 

Which  disk  to  show  me  -|-,  ^,  \,  ^,  and  -^? 

Which  disk  to  show  me  ^,  -f ,  and  ^  ? 

Which  disk  to  show  me  ^,  \,  \,  and  y^^? 

Which  disk  to  show  me  ^,  ^^  ^,  and  ^? 

Which  disk  to  show  me  ^,  \,  and  I? 

I  have  blocks  which  are  3,  4,  and  6  inches  long.  What 
must  be  the  length  of  the  shortest  box  into  which  they 
exactly  fit  ? 

Find  the  shortest  length  of  plank  that  I  must  buy  if  I 
wish  to  cut  it  into  pieces  3  feet,  6  feet,  or  9  feet  long,  so 
that  there  will  be  no  waste. 

Find  the  narrowest  width  of  cloth  that  I  must  buy  if  I 
wish  to  cut  it  into  2  inch  squares,  3  inch  squares,  4  inch 
squares,  6  inch  squares,  8  inch  squares,  or  12  inch  squares, 
without  any  waste. 


CHAPTEE    XXXVIII. 

DECIMALS. 


§  88.     Tenths. 

Name  a  fraction  whose  denominator  is  ten.     Express  the 
fraction  on  the  board.     (^.) 

I  will  express  the  same  fraction.     (0.3.) 
Eead  what  I  have  expressed. 

Name  another  fraction  whose  denominator  is  ten.     Ex- 
press.    (^.) 

I  will  express  the  same  fraction.     (0.7.) 
Express  one-tenth  in  this  new  way.     (0.1.) 
We  call  it  the  decimal  way. 
Express  nine-tenths  the  decimal  way.     (0.9.) 
Express   two-tenths,    four-tenths,  five-tenths,  six-tenths, 
eight-tenths. 

Eead  what  you  have  expressed  as  I  point. 
Express  and  add  : 

One-tenth,  three-tenths,  four-tenths. 

Five-tenths,  two-tenths,  one-tenth. 

Seven-tenths,  one-tenth,  zero-tenths. 

Eight-tenths,  zero-tenths,  one-tenth. 

Six-tenths,  two-tenths,  one-tenth. 

Express  and  subtract : 

Eight-tenths  minus  three-tenths. 
Nine-tenths  minus  seven-tenths. 
Seven-tenths  minus  three-tenths. 
Nine-tenths  minus  six- tenths. 
Nine-tenths  minus  five-tenths. 


DECIMALS.  451 

Express  and  multiply : 

Four-tenths  by  two.  Two-tenths  by  three. 

Six-tenths  by  one.  Three-tenths  by  two. 

Two-tenths  by  four.  One-tenth  by  seven. 

Express  and  divide : 

Eight-tenths  by  two-tenths. 
Six-tenths  by  three-tenths. 
Eight-tenths  by  four-tenths. 
Nine- tenths  by  three-tenth- J. 
Six-tenths  by  two-tenths. 

Express  and  find : 

One-half  of  four-tenths ;    of  eight-tenths ;  of  six-tenths  ; 
of  two-tenths. 

One-third  of  six-tenths ;  of  three-tenths ;  of  nine-tenths. 
One-fourth  of  eight-tenths ;  of  four-tenths. 

Eead  what  I  have  expressed.     (32-j^.) 
Who  will  express  the  same  number  and  write  the  fraction 
the  decimal  way.     (32.3.) 

Write  decimally : 

Seven  and  six-tenths. 

Six  and  five-tenths. 

Eighteen  and  nine-tenths. 

Twelve  and  seven-tenths. 

Twenty  and  eight-tenths. 

Fifty  and  one-tenth. 

Three  hundred  and  twenty-four  and  four-tenths. 

Six  hundred  and  thirty  and  two-tenths. 

Express  and  add  : 

Eight-tenths,  seven-tenths,  five-tenths,  four-tenths,  seven 
tenths,  three-tenths. 


452  FIRST  STEPS   IN   NUMBER. 

Six-tentlis,  nine-tenths,  eight-tenths,  five-tenths,  seven- 
tenths,  four-tenths. 

Three-tenths,  seven-tenths,  nine-tenths,  three-tenths,  six- 
tenths,  two-tenths. 

Eleven  and  three-tenths,  five  and  seven-tenths,  eighteen 
and  nine-tenths,  twenty  and  eight-tenths. 

Express  and  subtract : 

Seven  and  five-tenths  minus  seven-tenths. 
Fifteen  and  three-tenths  minus  eight-tenths. 
Twenty-five  and  two-tenths  minus  sixteen  and  nine-tenths. 
Forty-two  and  five-tenths  minus  twenty  and  six-tenths. 
Sixty-five  and  seven-tenths  minus  thirty  and  eight-tenths. 

Express  and  multiply  : 

Eight- tenths  by  seven.  Nine-tenths  by  eight. 

Six-tenths  by  eight.  Seven-tenths  by  nine. 

Eight  and  seven-tenths  by  six ;  by  eight. 
Twelve  and  five-tenths  by  fourteen ;  by  nineteen. 

Express  and  divide : 

One  and  eight-tenths  by  nine-tenths. 
Twenty-seven  and  three-tenths  by  three-tenths. 
Fifty-six  and  eight-tenths  by  eight-tenths. 
Eighty-five  and  six-tenths  by  four-tenths. 
Seventy-seven  and  five-tenths  by  five-tenths. 
Ninety-eight  and  four-tenths  by  six-tenths. 

§  89.     Tenths  and  Hundredths. 

Name  a  fraction  whose  denominator  is  hundredths. 

Express  it  on  the  board,     (twu-) 

I  will  express  the  same  fraction.     (0.17.) 

Read  what  I  have  expressed. 


DECIMALS.  453 

Express  in  tliis  decimal  way  : 

Eighteen-hundredths ;  twenty-four  hundredths;  fifty- 
two  hundredths ;  seventy-four  hundredths ;  sixty-nine 
hundredths ;  ninety-seven  hundredths. 

Read  what  you  have  expressed  as  I  point. 

Look  at  this  number.  (0.13.)  When  I  hide  the  three 
so  that  you  see  only  the  point  and  one,  what  will  you  call 
the  number  you  see?  (0.1.)  One-tenth  equals  how  many 
hundredths?  Thirteen-hundredths  are  how  many  more 
than  one-tenth?  Read  the  number  then  in  tenths  and  hun- 
dredths. 

Read  in  tenths  and  hundredths  each  of  the  number  of 
hundredths  you  have  just  expressed  on  the  board. 

Read  this  number  in  tenths  and  hundredths.  (0.04.) 
This  number.     (0.05.) 

Express : 

Seven-hundredths ;  eight-hundredths  ;  one-hundredth ; 
three-hundredths  ;  two  hundredths  ;  six-hundredths ;  nine- 
hundredths. 

Read  what  you  have  expressed. 

Express  and  add : 

Three-hundredths,  eight-hundredths,  nine-hundredths, 
five-hundredths,  seven-hundredths. 

Nine-hundredths,  six-hundredths,  five-hundredths,  seven- 
hundredths,  five-hundredths. 

Sixteen-hundredths,  seven-hundredths,  thirteen-hun- 
dredths, thirty-six  hundredths,  four-hundredths,  fifteen- 
hundredths. 

Twenty-three  hundredths,  nineteen  hundredths,  seven- 
teen-hundredths,  eight-hundredths,  forty -hundredths,  fifty- 
hundredths. 

Three  and  five-hundredths,  seven  and  six-hundredths, 
nine  and  fifteen-hundredths,  six  and  fifty-four  hundredths, 
seven  and  sixty-three  hundredths. 


454  FIRST  STEPS   IN   NUMBER. 

Express  and  subtract : 

Nine-hundredths  minus  tliree-hundredths. 

Seven-hundredths  minus  four-hundredths. 

Fifteen-liundredths  minus  seven-hundredths. 

Seventeen-hundredths  minus  nine-hundredths. 

Forty-two  hundredths  minus  twenty-eight  hundredths. 

Ninety-five  hundredths  minus  sixty-seven  hundredths. 

Eight  and  seventy-two  hundredths  minus  five  and  fifty- 
four  hundredths. 

Seven  and  eighty-three  hundredths  minus  four  and 
thirty-eight  hundredths. 

Seventy-two  and  ninety-four  hundredths  minus  thirty- 
five  and  twenty-six  hundredths. 

Express  and  multiply : 

Nine-hundredths  by  seven. 
Eight-hundredths  by  nine. 
Seven-hundredths  by  eight. 
Twelve-hundredths  by  seven. 
Fifty-seven  hundredths  by  nine. 
Seventy-eight  hundredths  by  eight.   • 
Nine  and  sixty-seven  hundredths  by  forty-six. 
Six  and  forty-nine  hundredths  by  seventy-seven. 

Express  and  divide : 

Nine-hundredths  by  three-hundredths. 
Twenty-seven  hundredths  by  nine-hundredths. 
Forty-two  hundredths  by  seven-hundredths. 
Fifty-six  hundredths  by  eight-hundredths. 
Eighty-seven  hundredths  by  three-hundredths. 
Ninety-six  hundredths  by  sixteen-hundredths. 
One  and  thirty-six  hundredths  by  seventeen-hundredths. 
One  and  seventy-six  hundredths  by  sixteen-hundredths. 


DECIMALS.  455 

Express  and  add : 

Seventy-five  and  eight-tenths,  five  and  six-hundredths, 
tkree-tenths,  eight  and  sixty-seven  hundredths,  nine-hun- 
dredths,  seven  and  eight-tenths. 

Fifty-nine  and  sixty-eight  hundredths,  seventy-seven  and 
nine-hundredths,  eighty-five  and  seven-tenths,  ninety  and 
six-hundredths,  six  and  ninety-seven  hundredths,  eight- 
liundredths,  nine-tenths,  five,  eighty. 

Express  and  subtract : 

Twenty  minus  seven-tenths. 

Fifty  minus  eighteen-hundredths. 

Sixty  minus  nine-hundredths. 

Seventy  and  two-tenths  minus  nineteen-hundredths. 

Seven-tenths  minus  sixty-seven  hundredths. 

Express  and  multiply : 

Eight  by  seven-tenths. 

Sixteen  by  nine-tenths. 

Sixty-nine  by  eight-tenths. 

Seven  by  nine-hundredths. 

Eighty-seven  by  sixty-nine  hundredths. 

Five-tenths  by  seven-tenths. 

One  and  seven-tenths  by  nine-tenths. 

Two  and  eight-tenths  by  three  and  seven-tenths. 

Seven  and  nine-tenths  by  eight  and  seven-tenths. 

Express  and  divide : 

Two  by  one-tenth. 

Four  by  two-tenths. 

Eight  by  four-tenths. 

Twenty-seven  by  three-tenths. 

Two-tenths  by  one-hundredth. 

Six-tenths  by  three-hundredths. 

Seven  and  two-tenths  by  eight-hundredths. 


456 


FIRST  STEPS   IN   NUMBER. 


Thirty-seven  and  five-tenths  by  fifteen-hundredths. 

Nine  by  eighteen-hundredths. 

Seven  by  fourteen-hundredths. 

Eight  by  sixteen-hundredths. 

Five  and  one-tenth  by  seventeen-hundredths. 

Seven  and  two-tenths  by  twenty-four  hundredths. 

Express  either  in  tenths  or  in  hundredths: 


One-half. 

One-twentieth. 

One-fifth. 

Three-twentieths. 

Two-fifths. 

Seven-twentieths. 

Three-fifths. 

Nine-twentieths. 

Four-fifths. 

One  twenty-fifth. 

One-fourth. 

Twelve  twenty-fifths. 

Three-fourths. 

One-fiftieth. 

Find: 

0.3  of 

25. 

0.06    of    76. 

0.7  of 

63. 

0.09    of   89. 

0.9  of 

72. 

0.03    of   80. 

0.5  of 

84. 

0.05    of  100. 

0.4  of 

95. 

0.06    of  100. 

0.2  of 

79. 

0.06    of  200. 

0.6  of 

96. 

0.12    of  450. 

0.1  of  800. 

0.16    of  325. 

0.6  of  125. 

0.25    of  484. 

0.8  of  376. 

0.88|  of  100. 

0.9  of  284. 

0.66|  of  100. 

0.7  of  576. 

0.16f  of  100. 

Express  as  common  fractions,  and  reduce  to  lowest  terms  : 

0.5       0.2       0.8         0.08       0.04       0.12       0.16       0.50 
0.4       0.6       0.02       0.06       0.05       0.15       0.25       0.75 


DFCIMALS.  457 

Express : 

Two  dollars  and  thirty-six  cents  ($2.36) ;  twelve  cents 
($0.12);  one  dollar  and  five  cents;  five  dollars  and  one 
cent ;  three  dollars  and  twenty-one  cents ;  ten  dollars  and 
fifty  cents ;  fifty  dollars  and  ten  cents. 

Read  what  you  have  expressed. 

Express  and  add  : 

Three  dollars  and  twenty-five  cents,  one  dollar  and  fifty 
cents,  nine  cents,  thirty-six  cents,  five  dollars  and  thirty 
cents. 

Express  and  subtract : 

Six  dollars  and  fifty  cents  minus  three  dollars  and  thirty- 
two  cents. 

Eight  dollars  and  eighty-two  cents  minus  four  dollars 
and  forty-eight  cents. 

Five  dollars  minus  two  dollars  and  sixty-two  cents. 

Express  and  multiply  : 

Seven  dollars  and  fifteen  cents  by  seven. 
Eleven  dollars  and  four  cents  by  four. 
Eight  dollars  and  ten  cents  by  eight. 

Express  and  divide  : 

Ten  dollars  and  twelve  cents  by  two. 

Five  dollars  and  twenty-two  cents  by  three. 

Ten  dollars  and  eighty-four  cents  by  five  dollars  and 
forty-two  cents. 

Three  hundred  and  twenty-four  dollars  and  eight  cents 
by  one  dollar  and  seven  cents. 

Six  hundred  and  fifty  dollars  and  nine  cents  by  one  dol- 
lar and  two  cents. 

Nine  hundred  dollars  by  eighty  dollars. 


CHAPTER  XXXIX. 

PERCENTAGE. 


§  90.   Percentage. 

Express  on  the  board  one-hundredth  ;  four-hundredths  ; 
ten-hundredths ;  twenty-hundredths ;  twenty-five  hun- 
dredths ;  fifty-hundredths ;  seventy-five  hundredths. 

What  have  you  been  expressing  ? 

I  have  a  new  name  for  a  hundredth.  I  will  write  it. 
{jper  cent.)     What  is  it  ? 

One  per  cent  is  how  many  hundredths? 

Two  per  cent  is  how  many  hundredths  ? 

Eight  per  cent  is  how  many  hundredths  ? 

Fifty  per  cent  is  how  many  hundredths  ? 

One-hundredth  is  what  per  cent  ? 

Three-hundredths  is  what  per  cent  ? 

Fifteen-hundredths  is  what  per  cent  ? 

Eead  what  you  have  written,  giving  the  namep^r  cent. 

Write  what  you  have  read,  using  the  words  per  cent. 

Kead  these  per  cents,  giving  the  name  hundredths  : 

25    per  cent.  60    per  cent.  80    per  cent. 

40    per  cent.  90    per  cent.  2    per  cent. 

100    per  cent.  200    per  cent.  500    per  cent. 

33-|-  per  cent.  66|-  per  cent.  12^  per  cent. 

Two  per  cent  of  fifty  dollars  is  how  many  hundredths  of 
fifty  dollars? 

Two  per  cent  of  fifty  dollars  is  how  many  dollars  ? 


PERCENTAGE.  459 

Twenty-five  per  cent  of  eighty  dollars  is  how  many 
hundredths  of  eighty  dollars  ? 

Twenty-five  per  cent  of  eighty  dollars  is  how  many 
dollars  ? 

Find  five  per  cent  of  sixty ;  ten  per  cent  of  ninety ; 
seventy-five  per  cent  of  twenty-four ;  sixty  per  cent  of 
twenty  ;  fifty  per  cent  of  one  hundred  and  fifty. 

If  from  a  barrel  holding  40  gallons  of  vinegar  15  per 
cent  is  drawn  ofi",  how  many  gallons  are  drawn  ofi"? 

A  salesman  has  250  pieces  of  cloth.  If  4  per  cent  of  the 
number  of  pieces  is  imperfect,  how  many  pieces  are  im- 
perfect ? 

If  of  a  flock  of  300  sheep  3  per  cent  died,  how  many 
sheep  died  ? 

I  have  in  my  school  building  350  children.  If  on  a 
stormy  day  14|-  per  cent  of  the  number  is  absent,  how 
many  are  absent  ? 

If  of  50  words  which  you  write  2  per  cent  is  wrong, 
how  many  words  are  misspelled  ? 

If  I  give  you  25  examples  to  perform,  and  you  have  time 
for  only  80  per  cent  of  that  number,  how  many  do  you 
perform  ? 

I  have  a  box  containing  12  bunches  of  envelopes.  If  I 
use  16f  per  cent  of  the  envelopes,  how  many  bunches  do  I 
use  ? 

If  a  man  buys  a  house  for  $20,000,  and  sells  it  for  100 
per  cent  of  its  cost,  for  what  does  he  sell  it  ? 

If  you  have  20  words  to  spell,  and  spell  100  per  cent  of 
them  correctly,  how  many  do  you  spell  correctly  ? 

If  my  watch  cost  $  50,  and  I  sell  it  for  100  per  cent  of 
its  cost,  what  do  I  gain  ? 

If  thread  which  costs  5  cents  a  spool  is  sold  for  100  per 
cent  of  its  cost,  what  is  the  loss  per  cent  ? 

If  a  man  sells  a  horse  for  100  per  cent  of  its  cost,  what 
does  he  gain  ? 


460  FIRST  STEPS   IN   NUMBER. 

What  is  100  per  cent  of  any  number  ? 

Any  number  is  what  per  cent  of  itself? 

If  the  price  of  a  book  is  $1.50,  but  the  salesman  deducts 
2  per  cent  of  the  price,  how  much  does  he  get  for  the  book  ? 

If  I  lend  a  man  $200,  and  he  pays  me  6  per  cent  of 
it  for  the  use  of  it,  how  much  money  must  he  pay  me  when 
he  settles  the  note  ? 

If  you  go  to  school  75  per  cent  of  the  year,  how  many 
months  do  you  have  for  vacation  ? 

For  what  must  cloth  which  cost  a  dollar  a  yard  be  sold 
to  gain  1  per  cent  ? 

For  what  must  apples  which  cost  12  cents  a  dozen  be 
sold  to  gain  50  per  cent  ? 

For  what  must  confectionery  which  costs  20  cents  a  pound 
be  sold  to  gain  100  per  cent  ? 

For  what  must  soap  which  costs  32  cents  a  cake  be  sold 
to  gain  25  per  cent  ? 

A  basket  of  wood  which  weighed  50  pounds  stood  out  in 
the  rain.  When  wet  it  was  found  to  have  gained  20  per 
cent  in  weight.     How  much  did  it  weigh  then  ? 

A  quantity  of  sugar  which  weighed  75  pounds  was  found 
to  have  decreased  40  per  cent  in  weight  by  drying.  How 
much  did  it  then  weigh  ? 


Express  in  all  the  ways  you  can : 

1  per  cent.              5    per  cent.  16|  per  cent. 

2  per  cent.            12|-  per  cent.  20    per  cent. 
4  per  cent.            14-f-  per  cent.  25    per  cent. 

Here  is  a  sign  which  we  use  instead  of  the  words  per 
cent  (%). 

Express  each  of  the  above  per  cents  on  the  board,  using 
this  sign. 


PERCENTAGE.  461 

In  how  many  ways  can  you  now  express  a  per  cent? 
What  kind  of  a  fraction  is  a  per  cent  ? 
Express  each  of  these  per  cents  in  the  form  of  a  common 
fraction  reduced  to  lowest  terms  : 

25%.  16|%.  100%.  8%. 

20%.  75  %.  10%.  150%. 

50%.  12i%.  200%.  5%. 

Express  each  of  these  numbers  as  a  per  cent : 

h  h  I  tV.  ^.  ^.  ^.   1.  2,  3,  8,  li,  li,  11,  1^^, 

1^,   1^V>    l^V.   f.   i  T%  A.  tV   ^(T.   If.   If,   1- 

If  you  have  4  apples,  and  eat  2,  what  part  of  the  num- 
ber of  apples  have  you  eaten  ?  What  per  cent  have  you 
eaten  ? 

2  is  what  per  cent  of  4  ? 

If  you  have  20  cents,  and  spend  10  cents,  what  part  of 
your  money  do  you  spend  ?   What  per  cent  of  your  money  ? 

10  is  what  per  cent  of  20  ? 

A  merchant  has  a  piece  of  flannel  containing  25  yards. 
If  he  sells  12|-  yards,  what  fractional  part  of  the  whole 
does  he  sell  ?     What  per  cent  of  the  whole  does  he  sell  ? 

12^  is  what  per  cent  of  25  ? 

If  it  is  50  miles  between  two  places,  and  you  start  from 
one  of  the  places,  and  travel  25  miles  toward  the  other, 
what  part  of  the  distance  do  you  travel  ?  What  per  cent 
of  the  distance  do  you  travel  ? 

25  is  what  per  cent  of  50  ? 

If  I  teach  6  hours  in  the  day,  what  part  of  the  day  do  I 
teach  ?  What  per  cent  of  the  day  am  I  employed  in  teach- 
ing?_ 

6  is  what  per  cent  of  24  ? 

If  I  use  18  sheets  from  a  quire  of  paper,  what  part  of 
the  whole  do  I  use  ?     What  per  cent  of  the  whole  ? 

18  is  what  per  cent  of  24  ? 


462  FIRST  STEPS   IN   NUMBER. 

If  I  have  four  5-cent  pieces,  and  spend  one  of  them, 
what  part  of  my  money  do  I  spend  ?  If  I  spend  3  pieces, 
what  per  cent  do  I  spend  ? 

5  is  what  per  cent  of  20  ? 

15  is  what  per  cent  of  20? 

If  you  have  ten  2-cent  pieces,  and  spend  2  of  them,  what 
part  of  your  money  do  you  spend  ?  What  per  cent  of  your 
money  do  you  spend  ?  If  you  spend  5  of  them,  what  per 
cent  of  your  money  do  you  spend  ? 

4  is  what  per  cent  of  20  ? 

10  is  what  per  cent  of  20  ? 

If  a  man  earns  $25  a  week,  and  spends  $25  a  week, 
what  per  cent  of  his  earnings  does  he  spend  ? 

25  is  what  per  cent  of  25  ? 

If  a  man  sells  a  load  of  wood  for  $15,  which  cost  him 
$15,  what  per  cent  of  the  cost  is  the  selling  price? 

15  is  what  per  cent  of  15  ? 

If  you  buy  a  knife  for  $1,  and  sell  it  for  $1,  what  per 
cent  of  the  cost  is  the  selling  price  ? 

1  is  what  per  cent  of  1  ? 
40  is  what  per  cent  of  40  ? 
50  is  what  per  cent  of  50  ? 
90  is  what  per  cent  of  90  ? 

4  is  what  per  cent  of  4  ? 

2  is  what  per  cent  of  2  ? 
100  is  what  per  cent  of  100  ? 
200  is  what  per  cent  of  200  ? 

If  a  man  buys  shoes  for  $5  a  pair,  for  what  must  he  sell 
them  to  receive  a  hundred  per  cent  of  their  cost  ? 

5  is  100%  of  what  number? 

If  a  man  buys  sugar  at  8  cents  a  pound,  for  what  must 
he  sell  it  per  pound  to  receive  100%  of  its  cost? 
8  is  100%  of  what  number? 
12  is  100%  of  what  number? 


PERCENTAGE.  463 

25  is  100%  of  what  number? 

100  is  100%  of  what  number? 

A  jeweller  bought  a  pin  for  $2,  which  was  50%  of  what 
he  received  for  it.     For  what  did  he  sell  it  ? 

2  is  50%  of  what  number? 

Ida  spent  6  cents  this  morning,  which  was  50%  of  all 
the  money  she  had.     How  much  money  had  she  ? 

6  is  50%  of  what  number? 
9  is  50%  of  what  number? 
50  is  50%  of  what  number? 
100  is  50%  of  what  number? 
200  is  50%  of  what  number? 

In  your  class  there  are  12  children,  which  is  25%  of  the 
whole  number  in  the  room.     How  many  are  in  the  room  ? 

12  is  25%  of  what  number? 

A  man  gained  20  cents  on  a  book,  which  was  25%  of 
the  cost  of  the  book.     What  was  the  cost  of  the  book  ? 

20  is  25%  of  what  number? 

7  is  25%  of  what  number? 
9  is  25%  of  what  number? 
25  is  25%  of  what  number? 
50  is  25%  of  what  number? 
100  is  25%  of  what  number? 

In  selling  ladies'  hose,  a  merchant  lost  1  cent  on  a  pair, 
which  was  10%  of  the  cost.     What  was  the  cost? 

On  a  summer's  day  a  pint  of  water  evaporated  from  a 
tank.  If  this  was  5%  of  the  water  in  the  tank,  how  much 
water  was  there  in  the  tank  ? 

At  the  top  of  our  blackboard  there  is  a  strip  8  inches  in 
width  which  is  painted  green.  If  this  strip  is  20%  of  the 
whole  width  of  the  blackboard,  how  wide  is  the  blackboard  ? 

If  a  man  pays  $3  a  month  for  milk,  and  this  is  4% 
of  the  table  expenses  for  the  month,  what  are  the  table 
expenses  for  the  month  ? 


464  FIRST  STEPS   IN   NUMBER. 

A  man  paid  $2  for  the  use  of  some  money  for  one  month, 
and  this  was  1  %  of  the  sum  he  borrowed.  What  sum  did 
he  borrow  ? 

2  is    4%,  of  what  number? 

5  is    5%  of  what  number? 

1  is    2%  of  what  number? 

1  is    1  %  of  what  number  ? 

8  is  10%  of  what  number? 

7  is  20%  of  what  number? 

I  bought  a  book-case  for  |15,  and  sold  it  for  $18. 
What  per  cent  did  I  gain  ? 

There  were  20  children  in  the  class  at  the  beginning  of 
the  term,  but  there  are  only  15  now.  What  per  cent  of  the 
class  has  dropped  out  ? 

A  man  who  buys  apples  at  2  cents  sells  them  at  3  cents. 
What  per  cent  does  he  gain  ? 

If  bananas  cost  4  cents,  and  sell  at  7  cents,  what  is  the 
per  cent  of  gain  ? 

If  envelopes  cost  6  cents  a  bunch,  and  sell  for  12  cents  a 
bunch,  what  is  the  per  cent  of  gain? 

If  cloth  which  costs  $1  a  yard  sells  for  $1.05,  what  is 
the  per  cent  of  gain  ? 

If  goods  which  cost  $100  sell  for  $75,  what  is  the 
per  cent  of  loss? 

If  a  man  puts  $1000  into  business  at  the  beginning 
of  the  year,  but  finds  at  the  end  of  the  year  that  he  has 
but  $800,  what  is  his  per  cent  of  loss? 

If  75%  of  gun-powder  is  saltpetre,  what  per  cent  of  the 
whole  is  the  rest  of  the  mixture  ? 

If  25%  of  a  barrel  of  oil  is  drawn  off,  what  per  cent  is 
left  in  the  barrel  ? 

If  a  man  loses  10%  in  weight,  what  per  cent  of  his  former 
weight  is  his  present  weight  ? 

If  I  spend  90%  of  my  income  for  the  year,  what  per  cent 
of  my  income  do  I  save  ? 


PERCENTAGE.  465 

If  only  50%  of  grape  wine  is  pure  juice  of  the  grape, 
what  per  cent  is  adulteration  ? 

If  coffee  is  adulterated  15% ,  what  per  cent  is  pure  coffee  ? 

If  to  reduce  the  strength  of  vinegar  I  put  water  with  it 
so  that  85%  only  is  vinegar,  what  per  cent  is  water? 

If  70%  of  the  rock  in  New  England  is  granite,  what  per 
cent  is  not  granite  ? 

If  in  a  mixture  of  green  and  black  tea  30%  is  green  tea, 
what  per  cent  is  black  tea? 

If  a  man  sells  goods  at  120%  of  the  cost,  what  per  cent 
does  he  gain  ? 

If  goods  are  marked  down  to  75%  of  their  cost,  what  per 
cent  of  the  cost  is  the  reduction  ? 

§  91.   Commission  and  Brokerage. 

I  wish  to  hire  you  to  sell  some  fruit  for  me,  and  this  is 
the  bargain  I  will  make  with  you : 

You  shall  receive  2%  of  the  amount  of  money  you  bring 
me  from  the  sale  of  the  fruit. 

If  you  sell  20  crates  of  peaches,  at  $2.50  a  crate,  what 
will  you  receive  for  your  wages  ? 

If  you  sell  1000  boxes  of  grapes,  at  20  cents  a  box,  what 
shall  I  pay  you  ? 

How  much  will  you  receive  for  selling : 

100  barrels  of  apples,  at  $2  a  barrel  ? 

5  dozen  apricots,  at  15  cents  a  dozen  ? 

10  dozen  oranges,  at  3  cents  an  orange  ? 

40  boxes  of  raspberries,  at  25  cents  a  box  ? 

80  boxes  of  strawberries,  at  15  cents  a  box? 

20  dozen  bananas,  at  2  cents  each  ? 

Do  you  know  of  any  one  who  works  on  this  plan  ? 

When  any  person  is  engaged  to  work  for  another  on  these 
terms,  we  call  him  a  commission  agent. 


466  FIRST   STEPS   IN   NUMBER. 

The  money  which  he  receives  is  called  his  commission. 

You  sold  fruit  for  me  on  a  commission. 

I  will  make  you  my  agent  to  sell  other  goods  on  a  com- 
mission. 

If  you  sell  $1500  worth  of  butter,  at  4%  commission, 
what  shall  I  pay  you  ?   What  shall  I  receive  for  the  butter? 

If  you  sell  $500  worth  of  boots  and  shoes,  at  a  com- 
mission of  3%,  what  shall  I  receive  for  the  goods? 

If  you  sell  $350  worth  of  books,  at  a  commission  of 
21%,  and  pay  $5  for  freight  on  the  books,  what  shall  I 
receive  from  the  sale  of  the  books  ? 

What  ought  you  to  receive  for  buying  $900  worth  of 
goods  for  me,  at  a  commission  of  l|-%  ? 

If  an  agent  buys  $  2550  worth  of  fruit,  at  a  commission 
of  3|-%,  what  does  he  receive  for  his  work? 

If  an  agent  sells  25  sewing  machines,  at  $40  each,  and 
receives  a  commission  of  1|%  besides  his  expenses,  which 
are  $50,  how  much  does  the  owner  receive  from  the  sale 
of  the  machines  ? 

An  agent  received  $3000  to  invest  in  flour,  at  $5  a 
barrel.  How  many  barrels  could  he  buy  after  deducting 
his  commission  of  2%  ?  For  what  must  the  merchant  sell 
the  flour  per  barrel  so  as  to  receive  100%  of  the  cost?  For 
what  must  he  sell  the  flour  so  as  to  gain  20%  of  its  cost? 

If  a  man  sells  a  house  for  me  for  $1000,  what  do  I 
receive  of  the  amount  if  his  commission  is  4%  ?  If,  besides 
my  agent's  commission,  I  pay  $25  for  advertising,  what 
has  it  cost  me  to  sell  my  place  ? 

An  agent  sold  5000  pounds  of  cotton,  at  10  cents  a 
pound.  After  deducting  his  commission  of  2|-%,  what 
amount  of  money  had  he  which  belonged  to  his  employer  ? 
He  bought  cotton  cloth  with  this  money,  and  received  2|-% 
commission  for  buying.  After  deducting  his  commission 
for  buying,  how  many  yards  of  cloth,  at  6  cents  a  yard, 
did  he  buy  with  the  sum  that  remained  ? 


PERCENTAGE.  467 

§  92.   Interest. 

A  man  offers  to  take  you  as  a  partner  in  his  business  if 
you  will  contribute  $1000  to  the  capital  already  in  the 
business.  You  have  but  $500,  so  you  decide  to  borrow 
the  other  $500.  Can  you  have  the  use  of  that  money 
for  nothing  ?  What  do  you  think  you  must  do  about  it  ? 
You  are  right :  you  must  pay  for  the  use  of  it.  I  will  say 
you  pay  $30  for  the  use  of  it.  Who  knows  what  name 
we  give  to  the  sum  you  pay  for  the  use  of  the  money? 
What  interest  do  you  pay  on  the  $  500  ? 

What  do  you  mean  when  you  say  you  pay  $  30  interest  ? 

When  you  borrow  this  money,  the  man  of  whom  you 
borrow  does  not  say,  "  T  will  lend  it  to  you  for  $30"  ;  he 
says,  ''  I  will  lend  it  to  you  at  6%  interest."  What  is  the 
interest  on  $500,  at  6%  ? 

Suppose  you  have  to  pay  7%  interest  on  $500,  to  what 
will  the  interest  come  ? 

To  what  will  it  come  if  you  have  to  pay  5%  interest? 
9%  interest?  4%  interest?  3%  interest?  8%  interest? 

If  at  6%  you  pay  only  $30  for  the  use  of  $500,  do  you 
know  how  long  you  have  a  right  to  keep  the  money  ? 

You  are  right :  you  can  keep  it  but  1  year.  Rate  of 
interest  is  usually  reckoned  by  the  year. 

What  must  you  pay  if  you  keep  the  $500  2  years? 
3  years  ?  4  years  ?  5  years  ?  |-  of  a  year  ?  -I-  of  a  year  ?  f  of 
a  year  ?  ^  of  a  year  ?  -J-  of  a  year  ?  6  months  ?  4  months  ? 
2  months? 

The  amount  of  interest  which  you  must  pay  on  $500 
depends  upon  two  conditions.  Can  you  name  the  two  con- 
ditions ? 

At  6%,  what  is  the  interest  on  $250  for  2  years?  for 
|-  of  a  year  ?  for  3  months?  for  3  years  and  6  months?  At 
7%,  what  is  the  interest  for  the  time  mentioned  in  each 
case?     Find  the  interest  at  5%. 


468  FIRST  STEPS   IN   NUMBER. 

Find  the  interest  of : 

1.  1 150  for  2  years  6  months,  at  6%. 

2.  1310.60  for  3  years  4  months,  at  6%. 

3.  $60.25  for  4  years  2  months,  at  7%. 

4.  $100  for  6  years  6  months,  at  8%. 

5.  $420  for  6  months,  at  5%. 

6.  $550.50  for  1  year  3  months,  at  8%. 

7.  $836.75for  2years4months,  at  6%. 

8.  $740  for  3  years  2  months,  at  ^%. 

9.  $860.40  for  6  years  4  months,  at  6%. 

10.  $999.95  for  1  year  9  months,  at  6%. 

11.  $275  for  4  months,  at  7^%. 

12.  $350for  4years8months,  at  6%. 

13.  $200.50  from  Nov.  19  to  March  19,  at  i 

14.  $600  from  July  3  to  Jan.  3,  at  S%. 


If  you  keep  $500  one  year,  at  6%  interest,  what  amount 
of  money  must  you  pay  when  you  settle  the  note  ?  If  you 
keep  the  money  2  years,  and  make  no  payments  of  interest 
during  the  time,  what  amount  must  you  pay  when  you 
settle  the  note  ? 

To  what  will  $300 amount  in  4  years,  at  6%  interest? 

To  what  will  $  120.25  amount  in  3i  years,  at  7%  interest  ? 

To  what  will  $2000  amount  in  5  years,  at  4%  interest? 

How  do  you  find  the  amount  when  you  know  the  in- 
terest ? 

"What  do  you  mean  by  amount  f 

The  sum  of  money  which  is  borrowed  has  a  particular 
name.  Can  you  tell  me  what  it  is?  It  is  called  the  prin- 
cipal. 


PERCENTAGE,  469 

Name  the  principal  in  the  examples  I  have  just  given 
you  to  perform. 

Which  requires  less  time,  to  find  the  interest  or  to  find 
the  amount  of  any  principal  ? 

Which  is  the  greater  sum  ? 

Find  the  amount  of : 

1.  $50  for  3  years  2  months,  at  6%. 

2.  $35  for  4  years  6  months,  at  7%. 

3.  $90  for  1  year  3  months,  at  6%. 

4.  $125for  2years8months,  at  6%. 

5.  $375  for  6  years  9  months,  at  4|-%. 

6.  $480  for  5  years  3  months,  at  8%. 

7.  $720  for  7  years,  at  4%. 

8.  $650for  8years4months,  at  6%. 

9.  $300for  2years  2months,  at  6%. 

10.  $525.50  for  1  year  9  months,  at  6%. 

11.  $250  from  Jan.  1,  1880,  to  July  1,  1886,  at  6%. 

12.  $125.25  from  March  3,  1882,  to  Oct.  3,  1884,  at  6%. 

13.  $75.75  from  May  10  to  Sept.  10,  at  6%. 

14.  $85  from  Oct.  24  to  April  24,  at  6%. 

15.  $90.25  from  Dec.  20  to  Sept.  20,  at  7%. 

16.  $70.75  from  May  1  to  Jan.  1,  at  8%. 


I  paid  $24  for  the  use  of  $200  for  2  years.  I  want  you 
to  help  me  find  the  rate  of  interest.  If  I  paid  $24  for  2 
years,  what  was  the  interest  for  1  year?  ($12.)  $12  is 
what  part  of  $200?  (-^•)  -^  equals  what  per  cent? 
(6%.)     What  then  was  the  rate  of  interest  ? 

Could  you  have  found  what  per  cent  12  was  of  200  with- 
out reducing  the  fraction  ? 


470  FIRST  STEPS   IN   NUMBER. 

I  paid  $63  interest  on  $350  for  3  years.  Can  you  find 
the  rate  of  interest  ?  What  was  the  interest  for  1  year  ? 
($21.)  21  is  what  per  cent  of  350?  (6%.)  What  rate  of 
interest  did  I  pay  ? 

If  the  interest  on  $200  for  6  years  is  $84,  what  is  the 
rate  per  cent  ?  For  what  time  will  you  find  the  interest 
on  the  principal  first?  What  will  you  do  next?  What 
is  your  answer?     (7%.) 

The  interest  on  $500  for  6  months  is  $20.  I  wish  to 
know  the  rate  per  cent.  What  is  the  interest  on  the  prin- 
cipal for  1  year?     ($40.)     40  is  what  per  cent  of  500? 

%.)     What  is  the  rate  of  interest  ? 


Find  the  rate  per  cent : 

1.  When  the  interest  on  $50  for  2  years  is  $6. 

2.  When  the  interest  on  $405.25  for  1  year  is  $16.21. 

3.  When  the  interest  on  $600  for  4  years  is  $120. 

4.  When  the  interest  on  $425.25  for  6  months  is  $17.01. 

5.  When  the  interest  on  $375  for  4  months  is  $7.50. 

6.  When  the  interest  on  $25  for  1  year  is  $2. 

7.  When  the  interest  on  $75.50  for  10  years  is  $30.20. 

8.  When  the  interest  on  $100  for  1  year  is  $3. 

9.  When  the  interest  on  $200  for  6  months  is  $3. 

10.  When  the  interest  on  $50  for  2  years  is  $3. 

11.  When  the  interest  on  $450  for  3  years  is  $60.75. 

12.  When  the  interest  on  $600  for  3  months  is  $9. 

13.  When  the  interest  on  $1000  for  1  year  is  $60." 

14.  When  the  interest  on  $850  for  2  years  is  $102. 

15.  When  the  interest  on  $725.50  for  9  months  is  $43.53. 

16.  When  the  interest  on  $300  for  8  months  is  $12. 


PERCENTAGE.  471 

I  borrowed  $600,  at  5%  interest.  If  tlie  interest 
amounted  to  $60  for  the  time  I  kept  the  principal,  can 
you  tell  me  how  long  I  kept  it  ?  You  may  first  tell  me 
what  would  be  the  interest  on  $600,  at  the  given  rate, 
for  1  year.  ($30.)  If  the  interest  for  1  year  is  $30,  how 
many  years  will  it  require  to  make  the  interest  $60? 
(2  years.)     How  long  then  did  I  keep  the  principal  ? 

If  the  interest  on  $25,  at  8%,  was  $4,  how  long  was 
the  principal  on  interest?  What  will  you  first  find? 
Having  found  the  interest  for  1  year  to  be  $2,  what 
will  you  do  to  find  how  many  years  the  principal  was  on 
interest  to  gain  $4? 

The  interest  on  $425.25,  at  8%,  was  $51.03.  How  long 
was  the  money  on  interest?  What  was  the  interest  for 
1  year?  ($34.02.)  How  long  then  was  the  money  on 
interest  to  gain  $51.03?     (1-^  years.) 

A  man  paid  $60.75  for  the  use  of  $450,  at  ^%  interest. 
How  long*  did  he  keep  the  principal?  For  what  length 
of  time  will  you  first  find  the  interest?  What  then  will 
you  do  to  find  the  time  ? 

Find  the  time  in  which  : 

1.  The  interest  on  $200  will  amount  to  $30,  at  6%. 

2.  The  interest  on  $275.50  will  amount  to  $38.57,  at  6%. 

3.  The  interest  on  $475  will  amount  to  $99.75,  at  7%. 

4.  The  interest  on  $500  will  amount  to  $82.50,  at  4J%. 

5.  The  interest  on  $60  will  amount  to  $168.55,  at  1i%. 

6.  The  interest  on  $100  will  amount  to  $22,  at  6%. 

7.  The  interest  on  $50  will  amount  to  $40,  at  8%. 

8.  The  interest  on  $  1000  will  amount  to  $975,  at  71% . 

9.  The  interest  on  $850  will  amount  to  $136,  at  6%. 
10.  The  interest  on  $700  will  amount  to  $70,  at  5%. 


472  FIRST  STEPS   IN   NUMBER. 

11.  The  interest  on  $625.25  will  amount  to  $75.03,  at  4%. 

12.  The  interest  on  $575.50  will  amount  to  $17.26i  at  6%. 

13.  The  interest  on  $350.50  will  amount  to  $12.22,  at  8%. 

14.  The  interest  on  $75.50  will  amount  to  $20.74,  at  7%. 

15.  The  interest  on  $90  will  amount  to  $4.50,  at  7i%. 

16.  The  interest  on  $900  will  amount  to  $54,  at  6%. 


I  kept  a  sum  of  money  2  years,  and  paid  $6  interest 
at  6%.  I  want  you  to  tell  me  what  the  sum  was.  You 
may  first  tell  me  what  I  should  pay  for  $  1  for  the  given 
time  at  the  given  per  cent.  (12  cents.)  If  $1  gained 
12  cents,  how  many  dollars  must  I  have  had  to  gain  $6 
interest?     ($50.) 

A  certain  sum  of  money  produced  $99.75  in  3  years,  at 
7%.  Let  us  see  if  we  can  find  the  sum.  What  would 
$1  produce  in  the  given  time  at  the  given  rate  ?  (21  cents.) 
If  $  1  produced  21  cents,  what  sum  was  required  to  produce 
$99.75?    ($475.) 

"What  sum  of  money  must  I  put  in  the  bank  that  in  10 
years  will  produce  $600,  at  6%  ?  What  will  you  first  find  ? 
Having  found  that  $1  for  the  given  time  at  the  given  rate 
produces  60  cents,  how  will  you  find  what  sum  will  pro- 
duce $600  in  the  same  time  at  the  same  rate?  What  sum 
do  you  find?     ($1000.) 

Find  the  principal  that : 

1.  Will  produce  $24  interest  in  3  years,  at  4%. 

2.  Will  produce  $45  interest  in  2J-  years,  at  6%. 

3.  Will  produce  $17.50  interest  in  |  year,  at  7%. 

4.  Will  produce  $84  interest  in  2^  years,  at  6%. 


PERCENTAGE.  473 

5.  Will  produce  $128  interest  in  4  years,  at  8%. 

6.  Will  produce  $31.50  interest  in  9  months,  at  6%. 

7.  Will  produce  $22.50  interest  in  3  years,  at  7-^%. 

8.  Will  produce  $35  interest  in  1^  years,  at  8%. 

9.  Will  produce  $75  interest  in  2  years,  at  5%. 

10.  Will  produce  $231  interest  in  7  years,  at  4%; 

11.  Will  produce  $297  interest  in  5^  years,  at  6%. 

12.  Will  produce  $13.75  interest  in  1  year,  at  5^%. 

13.  Will  produce  $8  interest  in  f  year,  at  8%. 

14.  Will  produce  $51.25  interest  in  3^  years,  at  6%. 


Just  a  year  ago  to-day  I  put  a  sum  of  money  in  the  bank, 
at  6%  interest.  That  sum  now  amounts  to  $106.  I 
want  you  to  find  what  sum  I  put  in  the  bank.  If  I  had 
put  in  $1,  what  would  it  have  amounted  to?  ($1.06.) 
If  $1  would  have  amounted  to  $1.06,  can  you  not  tell 
what  sum  I  must  have  deposited  to  amount  to  $106? 
($100.) 

I  have  just  deposited  a  sum  of  money  in  the  bank,  at 
6%  interest.  If  it  remains  there  2^  years,  it  will  amount 
to  $230.  What  is  the  sum  of  money  which  I  have  just 
deposited?     ($200.) 

If  to-day  you  put  out,  at  7%  interest,  a  sum  which  in 
3  years  will  amount  to  $363,  what  is  the  sum  at  interest? 
($300.) 

What  sum  in  3  years  and  4  months,  at  9%  interest,  will 
amount  to  $325?     ($250.) 

When  John  was  5  years  old,  his  father  put  a  sum  of  money 
in  the  bank  for  him,  at  6%  interest.  When  he  was  12 
years  old,  the  sum  had  amounted  to  $213.  What  was 
the  sum  deposited  ?     ($150.) 


474  FIRST   STEPS    IN    NUMBER. 

If,  at  the  age  of  a  year  and  four  months,  a  sum  of  money- 
was  put  at  interest  for  me  at  6%,  and  when  I  was  18  years 
old  it  had  amounted  to  $1000,  what  was  the  sum?  ($500.) 

Henry  has  a  sum  of  money  given  him  on  his  fifth  birth- 
day, which  he  lent  to  his  father,  at  6%  interest.  In  16 
years  8  months  it  had  amounted  to  $  10.  What  was  the 
sum  given  him?     ($5.) 

If  to-day  I  invest  a  sum  of  money  in  railroad  bonds,  at 
7%  interest,  which  will  amount  to  $745  in  7  years,  can 
you  tell  me  the  sum  I  invest  ?     ($500.) 

A  man  has  a  sum  of  money  invested  in  mortgages  which 
yield  him  1  %  a  month.  If  in  8  years  4  months  the  sum 
amounts  to  $2000,  what  is  the  sum  invested  ?    ($1000.) 

If  you  have  a  sum  of  money  invested  in  government 
bonds  which  yields  you  5%  interest,  and  in  5  years  it 
amounts  to  $  1000,  what  is  the  sum  invested  ?     ($800.) 

Find  the  principal  that  will  amount : 

1.  To  $868  in  4  years,  at  6%. 

2.  To  $1083  in  3  years  6  months,  at  4%. 

3.  To  $555  in  5  years  4  months,  at  9%. 

4.  To  $795  in  9  months,  at  8%. 

5.  To  $918  in  2  months,  at  12%. 

6.  To  $404  in  3  months,  at  4%. 

7.  To  $598  in  8  months,  at  6%. 

8.  To  $4000  in  12  years  6  months,  at  8%. 

9.  To  $2000  in  16  years  8  months,  at  6%. 


Presswork  by  Ginn  &  Co.,  Boston. 


